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C2.2 · Plan and justify an automobile route

Learn to plan and justify an automobile route through clear examples and targeted practice.

Ontario Grade 11 Mathematics

Transportation and Travel

Compare route choices and support your plan with clear reasons.

A route is the path from a starting point to a destination. A map or route-planning app may offer several choices. The shortest route is not always the most useful: another route may take less time, avoid a toll, or better suit the trip. Planning means comparing the choices and selecting one that fits the trip. To justify your choice, give reasons based on route information. Estimates can change with traffic, weather, or road work, so check current conditions before leaving.

What you will learn

Start with the trip’s needs

First, identify the starting point and destination. Decide when you need to arrive and what matters most. A work trip may have a firm arrival time. A weekend outing may focus on keeping costs low. These priorities tell you which route details to compare.
A route estimate is a useful prediction, not a promise. Travel time may change because of traffic, weather, construction, or a stop. Check a current map or route-planning tool close to departure. Look for delays, closures, tolls, and roads that may not suit your vehicle. A toll is a fee for using a particular road.
Record the same details for each route. Distance, estimated driving time, and tolls are often useful. If you are comparing costs, also note the vehicle’s fuel use and the fuel price. Keeping the information in a simple list or spreadsheet makes the comparison easier to follow.

Estimate fuel use and driving cost

Distance tells you how far you will drive. Travel time tells you how long the trip is expected to take. These are different measures: a longer route may have a shorter time estimate. Use the route tool’s estimate rather than guessing from distance alone.
Fuel consumption is the amount of fuel a vehicle uses over a set distance. It is often listed as litres per 100 kilometres. To estimate fuel for a route, multiply the route distance by the fuel-use rate, then divide by 100. Dividing by 100 adjusts the rate to the actual route distance. To estimate fuel cost, multiply the estimated litres by the price per litre. Add any toll to compare the stated driving costs.
A calculator or spreadsheet can help. Enter each route’s distance, time, toll, estimated fuel use, and cost. Use the same fuel-use rate and fuel price for each route when they apply to the same vehicle and trip. Keep extra digits during the calculation, then round money to the nearest cent. Fuel use and prices can vary, so describe the result as an estimate.
litres=distance×rate÷100\text{litres} = \text{distance} \times \text{rate} \div 100

Choose a route and explain why

Choose based on the trip’s main priority. If arriving soon matters most, compare estimated times and leave a buffer for possible delays. If keeping costs low matters most, compare estimated fuel costs and tolls. A route with a closure or an unsuitable road may not be a practical choice, even if it is short.
A clear justification names the route and connects evidence to the trip’s needs. For example: “I would take Route A because its estimated driving cost is lower, and I have enough time for the longer trip.” You can also explain a trade-off: “Route B is faster, but it costs more.” This shows how the evidence supports your decision.
Before leaving, check the route again. A new delay or closure may change which option fits best. Update your plan if needed. When arrival time matters, plan to leave early enough to allow for changing conditions.

Record a usable plan

A practical plan should be easy to follow. Record the start, destination, route name or main roads, estimated distance and time, and any toll. Include departure and arrival times if timing matters. If using a phone for directions, set it up before driving and follow road rules.
Separate estimates from confirmed information. A map’s travel time is an estimate. A published toll amount is a stated charge. Identify the values you used so another person can understand your comparison. A short written reason makes the route choice clear.
Different drivers may have different priorities, so there may not be one best route for every trip. State what matters, use current information, and explain the trade-off. That is how you plan and justify an automobile route.

Route comparison record

DetailRoute ARoute B
Distance84 km96 km
Estimated time1 h 12 min1 h 5 min
Fuel estimate7.056 L8.064 L
Estimated fuel costCAD 11.43CAD 13.06
Main advantageLower fuel costShorter estimated time

Worked example

Example 1: A work trip with a firm arrival time

A driver must reach a job site by 8:30 a.m. Route A is 84 km and is estimated to take 1 hour 12 minutes. Route B is 96 km and is estimated to take 1 hour 5 minutes. The vehicle uses 8.4 L per 100 km. Fuel costs CAD 1.62 per litre, and neither route has a toll. Which route fits best if arriving on time matters most? Compare estimated fuel costs too.
  1. Compare estimated times
    Route B has the shorter time estimate. The difference is 7 minutes, so it better fits the main priority. The driver should still leave a buffer for traffic.
    72−65=7 minutes72 - 65 = 7\text{ minutes}
  2. Estimate Route A fuel use
    The fuel rate is given for each 100 km. Multiply by the route distance and divide by 100 to estimate the fuel for this trip.
    84×8.4÷100=7.056 L84 \times 8.4 \div 100 = 7.056\text{ L}
  3. Estimate Route B fuel use
    Use the same vehicle rate for a fair comparison. Route B is longer, so its estimated fuel use is higher.
    96×8.4÷100=8.064 L96 \times 8.4 \div 100 = 8.064\text{ L}
  4. Compare fuel costs
    Multiply each fuel estimate by the price per litre. Round the final costs to the nearest cent.
    7.056×1.62=11.43072 CAD;8.064×1.62=13.06368 CAD7.056 \times 1.62 = 11.43072\text{ CAD};\quad 8.064 \times 1.62 = 13.06368\text{ CAD}
Answer: Choose Route B if arriving on time matters most. It is estimated to take 1 hour 5 minutes, 7 minutes less than Route A. Its estimated fuel cost is about CAD 13.06, compared with about CAD 11.43 for Route A.
Check: Route B is faster but costs more in fuel. Check current traffic and allow extra time before leaving.

Worked example

Example 2: A weekend trip with a cost priority

A driver wants to keep driving costs low. Route X is 132 km, takes an estimated 1 hour 48 minutes, and has no toll. Route Y is 118 km, takes an estimated 1 hour 55 minutes, and has a toll of CAD 6.25. The vehicle uses 9.1 L per 100 km, and fuel costs CAD 1.58 per litre. Which route has the lower estimated driving cost?
  1. Estimate Route X fuel use
    Multiply the route distance by the vehicle’s fuel-use rate and divide by 100 because the rate is stated per 100 km.
    132×9.1÷100=12.012 L132 \times 9.1 \div 100 = 12.012\text{ L}
  2. Estimate Route Y fuel use
    Apply the same rate to Route Y. Its shorter distance gives a lower fuel estimate, but its toll must also be included.
    118×9.1÷100=10.738 L118 \times 9.1 \div 100 = 10.738\text{ L}
  3. Find each route’s driving cost
    Multiply estimated litres by the fuel price. Add Route Y’s toll. Route X has no toll to add. The unrounded totals are rounded to the nearest cent.
    12.012×1.58=18.97896 CAD;10.738×1.58+6.25=23.21604 CAD12.012 \times 1.58 = 18.97896\text{ CAD};\quad 10.738 \times 1.58 + 6.25 = 23.21604\text{ CAD}
  4. Make the choice
    Route X has the lower estimated driving cost. It also has the shorter time estimate in this comparison, despite its greater distance.
Answer: Choose Route X for the lower estimated driving cost: about CAD 18.98, compared with about CAD 23.22 for Route Y. Route X is estimated to take 1 hour 48 minutes, 7 minutes less than Route Y.
Check: Route Y’s toll is included in its total. Leaving it out would give an incomplete cost comparison.

Common mistakes and how to avoid them

Choosing the shortest route automatically.
Correction: Compare time, cost, tolls, and current road conditions with the trip’s priorities.
Forgetting to divide by 100 when the fuel-use rate is per 100 km.
Correction: Divide the distance-times-rate result by 100 to estimate fuel for the route.
Leaving a toll out of the cost comparison.
Correction: Add the toll to estimated fuel cost when comparing driving costs.
Treating a map’s time estimate as guaranteed.
Correction: Treat it as an estimate, check conditions before departure, and allow a buffer when timing matters.

Lesson summary

Check your understanding

Question 1

A trip is 75 km. The vehicle uses 8 L per 100 km. About how many litres are needed for the trip?
  1. 6 L
  2. 8 L
  3. 10.7 L
  4. 60 L
Show answer and explanation
6 L
Multiply 75 by 8, then divide by 100. The estimate is 6 L.

Question 2

Route A is estimated at 50 minutes with no toll. Route B is estimated at 42 minutes and has a CAD 5 toll. If arriving sooner is the top priority and both routes are open, which route fits that priority?
  1. Route A, because it has no toll
  2. Route B, because its estimated time is shorter
  3. Route A, because it is always safer
  4. There is not enough information to compare estimated time
Show answer and explanation
Route B, because its estimated time is shorter
Route B has the shorter estimated time. Its toll matters when comparing cost, but the stated top priority is arriving sooner.

Question 3

What should you do if a current map shows a closure on your planned route?
  1. Follow the original plan because it was chosen first
  2. Ignore the closure if the route is shorter
  3. Recheck available routes and update the plan
  4. Assume the time estimate includes every future change
Show answer and explanation
Recheck available routes and update the plan
A closure can make the planned route unsuitable. Recheck current options and revise the plan before leaving.

Key terms

Route
A path from a starting point to a destination.
Fuel consumption
The amount of fuel a vehicle uses over a stated distance.
Toll
A fee charged for using a particular road.
Estimate
A useful prediction that may differ from the final result.
Justify
Give clear reasons and evidence to support a choice.

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About this lesson

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Mathematics (MEL3E), expectation C2.2. It is a study resource, not an official curriculum publication.

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