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C3.3 · Interpret routes, schedules, and fares for public travel

Learn to interpret routes, schedules, and fares for public travel through clear examples and targeted practice.

Ontario Grade 11 Mathematics

Transportation and Travel

Reading routes, schedules, and fares

A trip to work, school, or an appointment often depends on three questions: Which route should I take? When does it leave and arrive? How much will it cost? Public-travel documents give different parts of the answer. A route map or list shows where a vehicle goes. A schedule shows when it serves each stop. A fare chart explains what riders pay. This lesson uses a fictional transit service so you can practise reading all three without needing a particular city's rules.

What you will learn

Use a route map or route list to identify a suitable public-travel route.
Read a schedule to choose a departure and estimate an arrival time.
Interpret fare information to determine the cost of a trip.
Compare travel choices using the route, time, and fare information provided.

1. Find a route that serves your trip

A route is the path followed by a bus, train, or other public vehicle. A route number or name helps distinguish it from other services. A stop is a place where passengers can board or leave. A transfer means changing from one route or vehicle to another during a trip.

Start by finding the place where your trip begins and the place where it ends. Check which routes serve those stops. A route that passes near both places may be useful, but check the direction too. A bus going north may not serve the same stops as one going south. On a map, follow the route line and read the direction labels. In a route list, compare the stop names and any notes about the service.

A route with a transfer can still be a good choice. Consider whether the transfer stop is easy to find and whether the schedule gives enough time to change vehicles. If the document does not provide transfer details, do not assume a connection is guaranteed. Use the information shown, and check with the transit provider when an important detail is missing.

Match both the starting stop and destination to the route.
Check the direction of travel and any route notes.
A transfer means changing routes or vehicles.

2. Read a schedule and estimate travel time

A schedule lists times for a service. A row may show stops, while columns show different trips or departure times. Read the labels first: they tell you which stop and direction the times refer to. A listed time is usually the time the vehicle is scheduled to serve that stop, not a promise that it will never be delayed.

To plan a trip, find the time at your starting stop and then follow that same trip to the destination stop. The difference between those times is the scheduled travel time. For example, if a trip leaves at 8:12 a.m. and reaches the destination at 8:39 a.m., the scheduled time between stops is 27 minutes. You can count forward on a clock or use a calculator. Make sure you compare times from the same trip column.

Before choosing a departure, compare it with the time you need to arrive. Allow time to walk to the stop and, when needed, to transfer. If a schedule gives only selected times or says that service runs at regular intervals, use the information actually provided. Do not treat a frequency such as “every 20 minutes” as an exact arrival time at every stop.

Read the stop, direction, and trip labels before using a time.
Compare departure and arrival times from the same trip.
Allow time for getting to the stop and changing vehicles.

3. Interpret the fare information

A fare is the amount a rider pays for travel. A fare chart may list different prices for adults, youth, seniors, single rides, or day passes. Read the chart heading and notes to find which fare applies. A youth fare, for example, applies only if the rider meets the service's stated age rule.

A single-ride fare is the listed cost for one ride under the rules shown. A day pass is a ticket or payment option that may allow travel for a stated period or number of trips. Do not assume what a pass includes: check the chart for its rules, such as which routes it covers or when it expires. A transfer may be included with a fare, or it may have separate conditions. Use the fare document rather than guessing.

For more than one rider, multiply the applicable fare by the number of riders only if each rider pays that fare and the chart gives no group price. For repeated trips, add the costs of the trips that will actually be taken. A calculator or spreadsheet can help keep totals accurate. A spreadsheet is a grid in which you can enter trip costs and add them; it is useful when comparing several travel plans.

Compare the complete options, not just the lowest price shown. A less expensive fare may not cover the time or routes you need. A route that costs more may avoid a long wait or transfer. The best choice depends on the trip details and the fare rules.

Check rider category, fare type, and conditions.
Add or multiply costs only when the fare rules support that calculation.
Compare price with route and schedule needs.

4. Put the information together

A reliable travel plan connects the route, schedule, and fare. First, identify a route that serves your start and destination. Next, find a suitable departure and the scheduled arrival time. Then check the fare rules for the rider and trip. Finally, compare another available option if you need to balance arrival time, transfers, and cost.

Keep track of the details that can change the answer: travel direction, weekday or weekend service, a required transfer, and fare conditions. If the document is unclear or the trip is time-sensitive, confirm the information with the transit provider. Real services can change schedules and prices, so use the current information for the day you travel.

Use route, schedule, and fare information together.
Check whether the information applies to the day and direction of travel.
Confirm unclear details before relying on them.

Fictional Route 6 schedule: weekday trips

Stop	Trip A	Trip B
Library Stop	8:18 a.m.	8:36 a.m.
Community Centre	8:47 a.m.	9:05 a.m.

Worked example

Choose a departure and find the travel time

Maya needs to reach the Community Centre by 9:00 a.m. She can board Route 6 at Library Stop. The schedule below shows two trips that serve both stops. Which trip gets her there on time, and how long is its scheduled ride from Library Stop to Community Centre?

Read the trip columns
Each column is one trip, and each row names a stop. Compare times within one column so the departure and arrival belong to the same vehicle trip.
Check the arrival deadline
The first trip reaches the Community Centre at 8:47 a.m., before the 9:00 a.m. deadline. The second reaches it at 9:05 a.m., so it is too late.
Find the ride time
For the suitable trip, count from 8:18 to 8:47. There are 29 minutes between those times. This is the scheduled time between the two listed stops; it does not include Maya's walk to the Library Stop.
$8{:}47-8{:}18=29\text{ minutes}$

Answer: The 8:18 a.m. trip gets Maya to the Community Centre by 9:00 a.m. Its scheduled ride between the listed stops is 29 minutes.

Check: The arrival time, 8:47 a.m., is 13 minutes before 9:00 a.m., so it meets the deadline.

Worked example

Compare fares for a day's travel

Jordan will take Route 3 to work and Route 3 back home on the same day. The fictional fare chart lists a single ride at CAD 3.25 and a day pass at CAD 6.00. The chart says the day pass covers unlimited rides on Route 3 that day. Which option costs less for Jordan's two rides, and by how much?

Count the planned rides
Jordan plans two rides: one to work and one home. The chart gives a price for a single ride, so multiply that price by two to find the total for paying per ride.
$2\times\text{CAD }3.25=\text{CAD }6.50$
Check the pass conditions
The chart says the pass covers Route 3 for the whole day. Both planned rides are on that route and on the same day, so the pass applies to this plan.
Compare the totals
The two single rides cost CAD 6.50 altogether. The pass costs CAD 6.00, so subtract the pass price from the single-ride total to find the saving.
$\text{CAD }6.50-\text{CAD }6.00=\text{CAD }0.50$

Answer: The day pass costs less. Jordan saves CAD 0.50 by choosing it for the two Route 3 rides.

Check: Two single fares total CAD 6.50, which is CAD 0.50 more than the CAD 6.00 pass.

Common mistakes and how to avoid them

Using a time from one schedule column and an arrival time from another.

Correction: Follow one trip column from the starting stop to the destination so the times describe the same trip.

Assuming that any route passing near the destination serves the exact stop needed.

Correction: Check the listed stop names, direction, and route notes.

Choosing a pass because its name sounds suitable without reading its conditions.

Correction: Check the pass coverage, time period, and any other rules shown in the fare information.

Treating a scheduled time as a guarantee that there will be no delay.

Correction: Use the schedule to plan, and allow practical time for walking, transfers, and possible delays.

Lesson summary

Identify a route that serves the correct stops and direction.
Read schedule labels carefully and compare times from the same trip.
Use fare rules to choose the correct price and calculate trip totals.
Compare travel options using route, time, transfers, and cost.

Check your understanding

Question 1

A trip leaves a stop at 10:14 a.m. and reaches your stop at 10:42 a.m. in the same schedule column. What is the scheduled time between the stops?

18 minutes
28 minutes
42 minutes
56 minutes

Show answer and explanation

28 minutes

From 10:14 to 10:42 is 28 minutes. Subtract the minutes after checking that both times belong to the same trip.

Question 2

A route list shows that a bus serves your destination only when travelling east. What should you check before boarding?

Whether the bus is travelling east
Whether another route has a lower number
Whether the bus leaves at noon
Whether the fare chart lists a day pass

Show answer and explanation

Whether the bus is travelling east

The route serves the destination in the eastbound direction, so confirm the direction before boarding.

Question 3

A single ride costs CAD 2.80. What is the total for three single rides at that fare?

CAD 5.60
CAD 7.40
CAD 8.40
CAD 8.60

Show answer and explanation

CAD 8.40

Three rides at CAD 2.80 each cost CAD 8.40.

Key terms

Route: The path followed by a public vehicle, usually identified by a name or number.
Stop: A place where passengers can board or leave a public vehicle.
Schedule: A list or table showing when a service is planned to reach stops.
Fare: The amount a rider pays for public travel.
Transfer: A change from one route or vehicle to another during a trip.

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View the complete Ontario Grade 11 Mathematics learning path

About this lesson

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Mathematics (MEL3E), expectation C3.3. It is a study resource, not an official curriculum publication.

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