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C2.4 · Solve personal and business automobile-travel problems

Learn to solve personal and business automobile-travel problems through clear examples and targeted practice.

Ontario Grade 11 Mathematics

Transportation and Travel

Using distance, fuel use, and travel records for personal and business trips

A trip can involve more than getting from one place to another. You may need to estimate the fuel cost of a family visit or record kilometres driven for a work trip. In both cases, the answer depends on the information you are given. This lesson uses ordinary arithmetic and a calculator or spreadsheet. A fuel-use rating tells how many litres a vehicle uses for each 100 kilometres. A reimbursement rate tells how much an employer pays for each approved kilometre. Always use the rate or rule provided for the situation; do not assume that one rate applies everywhere.

What you will learn

Use trip information to find a travel distance.
Estimate fuel needed and fuel cost using a vehicle’s fuel-use rating.
Use a stated workplace reimbursement rate to calculate a business travel claim.
Check calculations and explain what the results mean.

1. Read the trip information

Start by identifying what you know and what you need to find. Useful details can include the trip distance, fuel-use rating, fuel price, odometer readings, and an employer’s reimbursement rate. An odometer is the display in a vehicle that records the total distance it has travelled.

If the trip distance is not given, you can find it from two odometer readings. Subtract the reading at the start from the reading at the end. The readings must be for the same vehicle and in the same units. The difference is the distance travelled between the readings.

For example, a start reading of 18,420 km and an end reading of 18,563 km show a trip distance of 143 km. If a trip has several parts, add the distances for those parts. This is useful when a driver stops at more than one work location.

Read the question carefully. A round trip includes travel to the destination and back. A one-way distance does not include the return journey. Also check whether a business travel record includes only work travel. Personal kilometres should not be added to a work claim unless the stated instructions say to include them.

d=r_2-r_1

Record the units, such as kilometres, litres, or CAD per kilometre.
Use the stated trip details and workplace rules.
Do not confuse a one-way distance with a return-trip distance.

2. Estimate fuel and fuel cost

A vehicle’s fuel-use rating is often written as litres per 100 kilometres. It is an estimate of how much fuel the vehicle uses over that distance. For example, a rating of 8.4 L/100 km means about 8.4 litres for each 100 kilometres travelled. Actual fuel use can vary with driving conditions, so the result is an estimate, not a promise of exact use.

To estimate fuel for a trip, compare the trip distance with 100 kilometres. Divide the distance by 100, then multiply by the vehicle’s rating. The answer is in litres. For instance, a 250 km trip is two and a half groups of 100 km. At a rating of 8 L/100 km, the estimate is 20 L.

To estimate the fuel cost, multiply the estimated litres by the price per litre. Keep extra decimal places while calculating, then round the final money amount to the nearest cent. Rounding too early can slightly change the result.

A calculator is suitable for a single trip. A spreadsheet can help with repeated trip calculations. Put the distance, fuel-use rating, and fuel price in separate cells. Use one calculation for estimated litres and another for cost. Check that the units in the cells match the information you entered. If the fuel price is entered as CAD per litre, the cost result will be in CAD.

L=\frac{d}{100}r

Fuel needed is an estimate based on distance and the vehicle’s rating.
Multiply estimated litres by the price per litre to find estimated fuel cost.
Round the final cost to the nearest cent.

3. Calculate and review a business travel claim

Some workplaces ask employees to record work-related kilometres and use a stated reimbursement rate. Reimbursement means money paid back for an approved expense. In a kilometre-based claim, multiply the approved distance by the rate given in the workplace instructions.

For example, if a workplace says to claim CAD 0.62 for each approved kilometre, use that rate for the recorded work distance. This rate is an example for a particular calculation, not a general rule. Follow the current instructions from the employer, because rates and rules may differ between workplaces.

A claim may also list other allowed trip expenses, such as parking, as separate items. Add those costs only if the workplace rules allow them. Keep receipts or other records if required. A clear record makes it easier to check the distance and the amount claimed.

Before using an answer, do a reasonableness check. A longer trip should use more fuel than a shorter trip if the vehicle rating stays the same. A higher fuel price should make the estimated cost higher. For a kilometre-based claim, check that the distance covers only the approved travel and that the rate was copied correctly. Also check that a cost is not being treated as a distance, or a distance as a cost.

C=kr

Use only the business distance and reimbursement rate provided for the situation.
Treat separately listed expenses according to the stated workplace rules.
Check units, records, and whether the result makes sense.

Trip information to gather

Question	Information to use	Unit or note
How far was the trip?	Trip distance or start and end odometer readings	km
How much fuel is estimated?	Distance and vehicle fuel-use rating	L and L/100 km
What is the estimated fuel cost?	Estimated litres and fuel price	CAD per litre
What is the kilometre-based claim?	Approved work kilometres and stated rate	CAD per kilometre

Worked example

Estimate fuel cost for a personal trip

A family plans a 286 km drive. Their vehicle’s fuel-use rating is 8.4 L/100 km, and fuel costs CAD 1.62 per litre. Estimate the fuel needed and its cost.

Find the number of 100 km groups
The rating is given for each 100 kilometres. Divide the trip distance by 100 to find how many such groups are in the trip.
$286\div100=2.86$
Estimate the litres needed
Multiply the number of 100 km groups by the fuel-use rating. This gives the estimated fuel in litres.
$2.86\times8.4=24.024\text{ L}$
Find the estimated cost
Multiply the estimated litres by the price for one litre. Keep the full estimate until the final step, then round the money amount to the nearest cent.
$24.024\times1.62=38.91888$

Answer: The trip is estimated to use about 24.024 L of fuel, costing about CAD 38.92.

Check: A 286 km trip is less than three 100 km groups, so the fuel estimate should be a little less than three times 8.4 L, or 25.2 L. The estimate of 24.024 L is reasonable. Multiplying that amount by CAD 1.62 per litre gives CAD 38.91888, which rounds to CAD 38.92.

Worked example

Prepare a simple business kilometre claim

An employee’s odometer reads 42,186 km before a work trip and 42,374 km afterward. The employer’s instructions allow CAD 0.62 per approved work kilometre and CAD 14.50 for this trip’s parking. Find the kilometre-based amount and the total including parking.

Find the work-trip distance
Subtract the starting reading from the ending reading. The difference is the distance recorded during the trip.
$42{,}374-42{,}186=188\text{ km}$
Calculate the kilometre-based amount
Multiply the approved distance by the rate in the employer’s instructions. This gives the amount based on kilometres.
$188\times0.62=116.56$
Add the allowed parking expense
The problem says this parking expense is allowed. Add it to the kilometre-based amount to find the total claim.
$116.56+14.50=131.06$

Answer: The kilometre-based amount is CAD 116.56. Including the allowed parking expense, the total is CAD 131.06.

Check: The distance is less than 200 km, so at CAD 0.62 per kilometre the kilometre-based amount must be less than CAD 124. The calculated amount, CAD 116.56, fits that check. Adding CAD 14.50 gives a total of CAD 131.06.

Common mistakes and how to avoid them

Using a one-way distance when the question asks for a return trip.

Correction: Check whether the stated distance already includes the return journey. If it does not, include both parts.

Multiplying kilometres directly by the fuel price.

Correction: First use the fuel-use rating to estimate litres. Then multiply litres by the price per litre.

Using an assumed reimbursement rate.

Correction: Use the rate and rules given in the problem or current workplace instructions.

Rounding intermediate results before finding the final cost.

Correction: Keep extra digits during the calculation and round the final money amount to the nearest cent.

Lesson summary

Use odometer readings or given trip details to find the distance.
Use the vehicle’s fuel-use rating to estimate litres, then multiply by fuel price.
For a kilometre-based business claim, multiply approved kilometres by the stated rate.
Include extra expenses only when the instructions allow them, and check that the result is sensible.

Check your understanding

Question 1

A vehicle uses 7.5 L/100 km. About how much fuel is needed for a 200 km trip?

7.5 L
15 L
27.5 L
150 L

Show answer and explanation

15 L

There are two groups of 100 km in 200 km, so the estimate is two times 7.5 L, or 15 L.

Question 2

A work trip is 125 km, and the stated rate is CAD 0.60 per kilometre. What is the kilometre-based amount?

CAD 20.83
CAD 75.00
CAD 125.60
CAD 750.00

Show answer and explanation

CAD 75.00

Multiply the approved distance by the rate: 125 times 0.60 is CAD 75.00.

Question 3

A trip’s estimated fuel use is 18 L, and fuel costs CAD 1.70 per litre. What is the estimated fuel cost?

CAD 10.59
CAD 19.70
CAD 30.60
CAD 180.00

Show answer and explanation

CAD 30.60

Multiply litres by the price per litre: 18 times 1.70 is CAD 30.60.

Key terms

Fuel-use rating: An estimate of how many litres a vehicle uses for each 100 kilometres.
Odometer: A vehicle display that records the distance it has travelled.
Reimbursement: Money paid back for an approved expense.
Reasonableness check: A quick check that an answer fits the situation and the information given.

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 11 Mathematics (MEL3E), expectation C2.4. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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