How to Apply Math to Understand Public Transportation Schedules

How to Apply Math to Understand Public Transportation Schedules

Introduction to Public Transportation Math

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Understanding Public Transport Schedules: A Math Adventure

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Math in Schedules: Time, Oh Time!

Public transport schedules are like a giant puzzle, and time is the key piece. In Secondary 1 Math Syllabus Singapore, you've learned about time, and it's exactly what you need here!

Fun Fact: The first MRT line, the North-South Line, was opened in 1987, transforming Singapore's public transport landscape.

Frequency and Intervals: Not Just for Music!

Remember learning about frequency in music? In public transport, frequency means how often a bus or MRT comes. Intervals, on the other hand, are the gaps between them. It's like a real-life pattern you can spot!

  • High frequency = more buses/MRTs = less waiting time
  • Low frequency = fewer buses/MRTs = more waiting time

Distance and Speed: The Race Against Time!

Now, let's add distance and speed to the mix. If you know how far you're going and how fast the bus or MRT is, you can calculate your travel time. It's like solving word problems, but with real-world implications!

Interesting Fact: The fastest MRT line in Singapore is the Thomson-East Coast Line, with a top speed of 80 km/h!

What if... You Missed Your Bus?

Life's not always perfect, and sometimes, you might miss your bus. What then? You calculate the next bus's arrival time, of course! It's all about finding patterns and making predictions, just like you do in math class.

So, the next time you're planning a trip, remember, you're not just looking at a schedule. You're solving a math problem. And that, my friend, is pretty cool.

Decoding Schedules with Time

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Time to Hop On: Navigating Public Transport Schedules

Imagine you're Ah Boy, a curious Secondary 1 student in Singapore, eager to explore the city after school. But first, you've got to crack the code on public transport schedules. Don't worry, we've got you covered with some math magic!

Time, Time, and More Time: The 24-Hour and 12-Hour Formats

Ever wondered why some bus schedules show times like 14:30 while others use 2:30 PM? They're both talking about the same time, just in different formats! The 24-hour format uses a 24-hour clock, while the 12-hour format splits the day into AM and PM. Let's decode these with a simple example:

  • 12:00 PM = 12:00 (noon)
  • 1:00 PM = 13:00
  • 12:00 AM = 00:00 (midnight)

Fun Fact: The 24-hour format is used worldwide, especially in the military and aviation, for its precision and clarity.

Military Time: When Minutes Matter

Now, let's step into the world of military time. It's just like the 24-hour format, but with an extra twist: no colon or AM/PM. So, 0730 is 7:30 AM, and 1900 is 7:00 PM. Why the fuss? Because every second counts when you're on duty!

History Lesson: Military time originated in the British Navy in the 18th century. It was later adopted by the U.S. military and has since become a global standard.

Real-World Applications: Public Transport Schedules

Now, let's put your newfound time knowledge to the test. You're planning to catch the MRT from Woodlands to Tampines. The schedule shows:

  • Woodlands to Boon Keng: 16:05
  • Boon Keng to Tampines: 16:35

What's the total travel time? That's right, it's 30 minutes! By understanding time formats, you've just mastered your first public transport schedule.

Secondary 1 Math Syllabus: Time and More

By the way, understanding time is a key part of the Secondary 1 Math Syllabus in Singapore. Keep practicing, and you'll be a time whiz in no time!

In the city-state of Singapore's structured secondary-level learning pathway, year two secondary students begin addressing advanced math concepts including quadratics, congruent figures, and handling stats, these develop from Secondary 1 basics and equip for higher secondary requirements. Parents often search for additional tools to enable their kids cope with the growing intricacy and keep steady advancement amidst educational demands. a level maths tuition delivers tailored , MOE-compliant sessions with skilled instructors who use interactive tools, real-life examples, and concentrated practices to enhance comprehension and assessment methods. The classes foster self-reliant resolution and address specific challenges like algebraic manipulation. Finally, these specialized programs enhances overall performance, alleviates stress, and sets a strong trajectory for O-Level achievement and future academic pursuits..

Interesting Fact: Did you know that Singapore's public transport network is one of the most efficient in the world? It's designed to keep waiting times short and connections seamless.

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Frequency and Intervals

Understanding Frequency

Frequency in public transportation is like the heartbeat of our city's veins. It measures how often a bus or train service arrives at a stop or station. In Singapore, with the secondary 1 math syllabus, you might learn about frequency as a representation of the number of times an event occurs within a fixed time interval. Here, the event is a bus or train, and the time interval is the time between two successive stops or stations.

Calculating Intervals

Intervals, on the other hand, are the pauses between beats. In the context of public transport, intervals are the time gaps between two consecutive buses or trains. Understanding intervals is key to planning your journey, especially during peak hours when intervals can be shorter due to increased demand. In the secondary 1 math syllabus, you'll learn to calculate intervals using frequency. For instance, if a bus comes every 15 minutes (frequency), then the interval is also 15 minutes.

Average Wait Time

Average wait time is the span of time you spend waiting for your bus or train. It's not just about the frequency or interval; it's also about when you arrive at the stop or station. If you arrive just after a bus has left, you might have to wait longer. In Singapore's hot and humid weather, every minute counts. So, understanding average wait time can help you plan your journey better. It's like estimating the time it takes for the next wave to crash onto the shore at East Coast Park.

Peak vs Off-Peak

Peak and off-peak periods are like day and night in the life of our public transport system. During peak hours, buses and trains are packed, and intervals are shorter to cope with the demand. In contrast, off-peak periods see fewer passengers and longer intervals. In the city-state of Singapore, the schooling system culminates early schooling years with a national examination which evaluates students' scholastic performance and determines future secondary education options. The test is administered on a yearly basis for students in their final year in primary school, emphasizing core disciplines for assessing comprehensive skills. The PSLE serves as a standard in determining entry into appropriate secondary courses depending on scores. It includes disciplines like English, Maths, Science, and Mother Tongue Languages, with formats refreshed occasionally to reflect educational standards. Scoring depends on Achievement Bands from 1 to 8, such that the aggregate PSLE mark represents the total of per-subject grades, influencing upcoming learning paths.. Understanding this rhythm can help you plan your journeys more efficiently. It's like knowing when to hit the sushi belt at Tanjong Pagar MRT station during lunch hour or late in the evening.

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Real-World Math

Math is not just about numbers on a page. It's about understanding and predicting real-world patterns. Public transportation is a perfect example. By applying what you've learned in your secondary 1 math syllabus, you can calculate frequencies, intervals, and average wait times. You can also predict how long you'll wait for your bus or train based on the time of day. It's like solving a puzzle, and every correct calculation gets you one step closer to your destination.

Journey Time and Distance

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Let's Get Rolling: Calculating Journey Times

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Imagine you're a secret agent, tasked with planning the perfect route to catch the earliest bus to your favourite roti prata stall before it gets too crowded. Sounds like a mission from a James Bond movie, right? But in reality, it's just another morning in Singapore, and you're about to apply some secondary 1 math to make your day run smoothly.

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First Things First: Distance and Time

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In the Secondary 1 Math Syllabus, you'll find that understanding the relationship between distance, speed, and time is crucial. It's like a magical formula that helps you predict when you'll reach your destination. The formula is simple, yet powerful:

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Time = Distance ÷ Speed

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Let's say your favourite roti prata stall is 5 km away, and you travel at an average speed of 20 km/h on the bus. Plug these numbers into the formula, and you'll find that the journey takes 15 minutes (or 0.25 hours). In Singapore's demanding schooling structure, Primary 3 marks a key change during which learners explore further into topics like multiplication facts, fraction concepts, and simple data analysis, expanding upon prior knowledge in preparation for more advanced critical thinking. Numerous families realize the speed of in-class teaching on its own might not be enough for every child, encouraging them to seek additional assistance to nurture math enthusiasm and prevent initial misunderstandings from developing. During this stage, personalized academic help becomes invaluable in keeping learning progress and fostering a development-oriented outlook. online tuition provides targeted, MOE-compliant guidance via group sessions in small sizes or individual coaching, focusing on heuristic approaches and visual aids to clarify complex ideas. Instructors commonly include gamified elements and frequent tests to monitor advancement and enhance drive. Finally, this early initiative also boosts current results and additionally establishes a solid foundation for thriving during upper primary years and the final PSLE exam.. Not too shabby, huh?

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Now, Let's Add Some Stops to the Mix: Journey Time with Stops

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But wait, what if your bus makes a few stops along the way? Don't worry, we can still calculate the total journey time. First, let's find the time spent moving between stops. If you make n stops, the time spent moving is:

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Time_moving = (Total_distance - Stop_distance) ÷ Speed

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For example, if your bus stops 3 times, and each stop adds 0.5 km to the total distance, the time moving between stops would be:

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Time_moving = (5 km - 1.5 km) ÷ 20 km/h = 0.2 hours

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Now, let's not forget the time spent at each stop. If each stop takes 1 minute, and you make 3 stops, the total stop time would be 3 minutes or 0.05 hours. Adding this to the time moving, your total journey time becomes:

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Total_journey_time = Time_moving + Total_stop_time = 0.2 hours + 0.05 hours = 0.25 hours

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So, even with stops, you'll still reach your favourite roti prata stall in 15 minutes. See, math isn't so scary after all!

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Fun Fact: The History of Public Transportation in Singapore

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Did you know that public transportation in Singapore started with horse-drawn carriages and trams in the late 19th century? It wasn't until the 1920s that buses started to appear. Today, our public transport network is one of the most efficient in the world, making it easier than ever to calculate journey times.

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Real-World Applications of Math: Public Transportation and Beyond

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The math you've learned today isn't just for catching the bus. It's also useful for planning your cycling route to school, calculating the time it takes for your mom to drive to the market, or even estimating how long it'll take for your package to arrive from an online shopping spree. The possibilities are endless!

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What If...?

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What if you could calculate the perfect time to leave the house to catch the bus, factoring in traffic, walking speed, and even the time it takes for the bus to fill up at each stop? Sounds like a job for some advanced math and programming, doesn't it? Maybe that's something to think about in secondary 2 or 3!

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So there you have it, folks. With just a little bit of secondary 1 math, you're now a public transportation scheduling whisperer. Now, go forth and conquer those bus stops, and remember, the key to successful time management is always having a well-fed tummy. Happy calculating!

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Ticket Pricing and Discounts

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Navigating Fares like a Pro: Real-World Math in Action

** *Hey there, secondary 1 parents and students! Ever wondered how to make sense of those public transport schedules and fares? Well, buckle up as we're about to embark on an adventure where math meets the MRT, and you'll be the hero who can navigate Singapore's public transport like a boss!* **

First Stop: Understanding Fares with Basic Math

** *You know how in your math syllabus, you've been learning about addition, subtraction, multiplication, and division? In the Republic of Singapore's performance-based education system, Primary 4 acts as a pivotal transition during which the curriculum escalates featuring subjects like decimals, balance and symmetry, and introductory algebra, challenging pupils to apply logical thinking in more structured ways. Many parents recognize the standard school sessions alone might not fully address individual learning paces, leading to the quest of additional resources to reinforce ideas and sustain ongoing enthusiasm with maths. As preparation for the PSLE increases, steady exercises becomes key in grasping these building blocks while avoiding overburdening child learners. best psle math tuition offers tailored , interactive tutoring aligned with Ministry of Education guidelines, integrating real-life examples, brain teasers, and digital tools to make theoretical concepts tangible and exciting. Seasoned instructors focus on spotting areas for improvement promptly and turning them into strengths via gradual instructions. Eventually, such commitment builds resilience, improved scores, and a seamless transition into upper primary stages, positioning pupils along a route to scholastic success.. These are your secret weapons to understanding public transport fares!* *Let's say you're taking the MRT from Ang Mo Kio to Jurong East. The fare is $2.20. But wait, you've got an EZ-Link card with $10. How much will you have left after your journey? Let's find out!* **

Fun Fact!

** *Did you know? The MRT network in Singapore is the longest in the world, with over 200km of tracks. That's more than the distance from the Merlion to the Malaysian border!* **

Next Stop: The Magic of Decimals

** *Now, let's talk about those pesky decimals. You might be thinking, "Why do I need to know decimals when I can just count by ones?" Well, hold on to your seats as we dive into the world of transfers and exact fares!* *Let's say you're taking a bus from your home to the MRT station. The fare is $0.90. Then, you take the MRT. The fare is $2.10. But if you make that bus ride within 15 minutes of tapping out at your first stop, you only pay $0.20 more! Can you guess how much you'll pay for the entire journey?* **

Interesting Fact!

** *Did you know? The first MRT line in Singapore, the North-South Line, opened in 1987. It was built with the help of Japanese technology, which is why the trains are known as "Trains to Tokyo" among the locals!* **

Boarding Pass: Applying Discounts

** *Now, let's talk about those lovely discounts. As a student or senior citizen, you get to enjoy concessionary fares. But how much exactly do you save? Let's find out using percentages!* *Let's say the adult fare is $2.50, and the student fare is $1.30. What's the discount percentage? Here's a hint: you can use the formula (Adult Fare - Student Fare) / Adult Fare * 100%.* **

History Lesson!

** *Did you know? The first bus services in Singapore were operated by rickshaws pulled by humans or horses! The first motorised bus service started in 1925, with a fare of just 5 cents.* **

The Grand Finale: Calculating Total Costs

** *Finally, let's put all your math skills together to calculate the total cost of a family day out! Let's say you're taking the MRT to Sentosa, then the cable car, and finally the tram. You've got your family of four, and you're all using your EZ-Link cards. What's the total fare, and how much will you save with the right combination of transfers and discounts?* *Now, it's time to put on your math detective hat and calculate! Remember, the key to mastering this is practice, practice, practice. So, keep working on those math problems, and soon you'll be navigating Singapore's public transport like a pro!* *And there you have it, folks! Math might not seem like the most exciting subject, but when you apply it to real-life situations like public transport, it can make all the difference. So, the next time you're planning a family outing or heading to school, remember that you're not just riding the MRT – you're navigating a real-world math adventure!*

Planning Routes and Transfers

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Navigating Singapore's Public Transport like a Pro: A Secondary 1 Math Adventure

Imagine you're Ah Boys to Men's Ken Chow playing a real-life game of Risk, strategizing your way across Singapore's public transport network. Sounds fun, right? Well, that's exactly what we're going to do, using none other than your Secondary 1 Math syllabus!

Mapping Your Journey: Graphs and Networks

Fun Fact: The MRT network is like a giant graph from your Math textbook, with stations as vertices and train lines as edges! To plan your route, you're essentially finding the shortest path in this graph.

Remember learning about adjacency matrices? Here's how it looks for a simple MRT network:

       A B C D     A 0 1 1 0     B 1 0 1 1     C 1 1 0 1     D 0 1 1 0     
In this matrix, a 1 means there's a direct train line between two stations.

Calculating Travel Time: Ratios and Proportions

Now, let's say you want to travel from Dhoby Ghaut to Tampines. You can take the MRT or the bus. But which is faster? Let's use ratios to find out!

As the Primary 5 level introduces a heightened degree of difficulty within Singapore's math curriculum, featuring ideas like proportions, percentage concepts, angles, and sophisticated problem statements demanding keener analytical skills, families often look for approaches to guarantee their children remain in front minus succumbing to typical pitfalls of confusion. This period is vital since it immediately connects with PSLE prep, where built-up expertise faces thorough assessment, necessitating timely aid essential in fostering resilience when handling multi-step questions. While tension escalating, dedicated assistance aids in turning likely irritations to avenues for advancement and expertise. primary math tuition singapore provides students via tactical resources and personalized mentoring matching Ministry of Education standards, using strategies such as diagrammatic modeling, graphical bars, and timed drills to explain intricate topics. Experienced educators emphasize clear comprehension instead of memorization, fostering dynamic dialogues and mistake review to instill assurance. At year's close, enrollees typically exhibit marked improvement in test preparation, paving the way for a stress-free transition to Primary 6 and beyond amid Singapore's rigorous schooling environment.. First, find the frequency of each service. Let's say buses come every 10 minutes and MRT trains every 5 minutes. The ratio of their frequencies is 2:1 (MRT to bus). This means you're twice as likely to catch an MRT train than a bus.

But what about trip duration? Let's say the MRT takes 25 minutes and the bus takes 40 minutes. The ratio of their travel times is 5:8 (bus to MRT). So, the bus takes 64% longer than the MRT.

Combining these ratios, we get an overall ratio of 4:8 (MRT to bus). This means the MRT is twice as fast as the bus for this particular journey.

Making Transfers: Sequences and Algorithms

Sometimes, you'll need to make transfers. Think of this as finding the next term in a sequence. For example, if you're at Bishan and want to go to Woodlands, you might take the MRT to Marina Bay and then switch to another line.

This is like an algorithm: Start at Bishan, take the MRT to Marina Bay, then take another MRT to Woodlands. Each step is a recursive call to the "find the next station" function.

Efficiency Matters: Optimization Problems

Did you know? The MRT system in Singapore is designed to minimize total travel time for all commuters. This is an optimization problem that transport planners solve using complex algorithms and mathematical models.

So, the next time you're planning your journey, remember you're not just finding a route - you're solving a real-world optimization problem, just like a transport planner!

And there you have it! From graphs to ratios, you've just applied your Secondary 1 Math syllabus to navigate Singapore's public transport like a boss. Now go forth, junior mathematicians, and conquer the MRT network!

Delay and Reliability

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Real-World Math: Navigating Public Transport Schedules

Secondary 1 Math Syllabus Singapore meets the real world as we explore how math can help us understand and navigate public transportation schedules in Singapore. Let's dive in!

Calculating On-Time Performance: The Bus Arrival Time Equation

Imagine you're waiting at the bus stop with your child. You both have a bus arrival time of 3:15 PM, but the clock is ticking and the bus is nowhere in sight. What's happening?

This is where on-time performance comes in. The bus arrival time can be calculated using the formula: Arrival Time = Scheduled Time + (Distance / Speed). If the bus is running late, the equation helps us understand why. For example, if the bus is scheduled to travel 5km at 20km/h, but it's only moving at 15km/h, it will arrive 5 / (20 - 15) = 10 minutes late.

Understanding Standard Deviation: The Bus On-Time Spread

Now, let's talk about standard deviation. You might be thinking, "What's that got to do with buses?" Well, it helps us understand how spread out the bus arrival times are.

For instance, let's say Bus A has an average delay of 5 minutes with a standard deviation of 2 minutes, while Bus B has an average delay of 10 minutes with a standard deviation of 5 minutes. In the city-state of Singapore's high-stakes educational setting, Primary 6 signifies the final phase in primary schooling, where pupils integrate years of learning in preparation for the vital PSLE exam, dealing with more challenging subjects like sophisticated fractional operations, proofs in geometry, problems involving speed and rates, and extensive study methods. Families often see that the jump of challenge may cause worry or knowledge deficiencies, especially regarding maths, motivating the requirement for expert guidance to polish abilities and exam techniques. In this pivotal stage, where all scores are crucial in securing secondary spots, supplementary programs become indispensable in specific support and confidence-building. mathematics tuition centre provides in-depth , centered on PSLE lessons matching the latest MOE syllabus, featuring practice tests, mistake-fixing sessions, and customizable pedagogy to address individual needs. Proficient tutors stress effective time allocation and higher-order thinking, aiding students tackle challenging queries with ease. All in all, this dedicated help also elevates results for the forthcoming PSLE and additionally instills self-control and a love for mathematics that extends into secondary education and further.. Although both buses are delayed on average, Bus A's delays are more consistent (less spread out) than Bus B's.

Comparing Reliability: The Tale of Two Bus Services

Let's meet two bus services: ExpressBus and LocalBus. ExpressBus has a consistent schedule, arriving every 15 minutes on the dot, while LocalBus arrives every 10-20 minutes due to traffic conditions.

Which one is more reliable? To find out, we can use the coefficient of variation (CV), which is the standard deviation divided by the mean. A lower CV means better reliability. For ExpressBus, the CV is 2 / 15 ≈ 0.13, and for LocalBus, it's 5 / 15 ≈ 0.33. ExpressBus is more reliable, despite its longer wait time!

Fun Fact: The World's First Double-Decker Bus

Did you know the world's first double-decker bus was introduced in 1855 in England? It was designed to carry more passengers and reduce crowding on the streets. Today, Singapore's double-decker buses are a common sight, carrying millions of passengers daily!

Thought-provoking Question: What if You Could Predict Delays?

Imagine if you could predict bus delays with perfect accuracy. You'd never miss a bus again! While we're not quite there yet, understanding math and statistics can help us make more informed decisions about our daily commute.

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Planning Multi-Stop Journeys

When planning a journey with multiple bus stops, you can apply the concept of addition and subtraction to calculate the total travel time. For instance, if the first bus takes 20 minutes and the second bus takes 30 minutes, you can add these times together to find the total travel time. Additionally, you can use the concept of multiplication to calculate the total travel time if you know the frequency of the buses and the number of stops.

Determining Wait Time

To calculate the wait time for the next bus, you can use the concept of remainders from division. If the current time is 10:45 AM and the next bus is due at 11:00 AM, you can calculate the wait time by subtracting the current time from the next bus time and applying the remainder concept.

Understanding Frequency of Buses

In the Singapore public transport system, buses run at different intervals. By applying the concept of frequency from the Secondary 1 Math syllabus, you can calculate the number of buses that arrive at a bus stop within a certain time frame. For example, if a bus arrives every 15 minutes, the frequency is 1 bus per 15 minutes, or 4 buses per hour.

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Frequently Asked Questions


Use the bus schedule and add the frequency interval (e.g., if the bus comes every 15 minutes, add 15 minutes to the last known arrival time).
Public transportation schedules often adjust for reduced demand on weekends, causing some bus timings to change.
Visit the public transportation authoritys website or use a mobile app to search for the route and view the schedule.
Loop indicates that the bus will return to its starting point after completing a circular route, typically with a different sequence of stops on the return journey.
Use the public transportation authoritys journey planner tool, which considers the schedules of multiple bus routes to help you plan your trip.