Motoring Mathematics: Costs, Fuel and Stopping Distances

Motoring mathematics

Running a car is about far more than the price on the windscreen. A driver has to work out what a vehicle really costs to buy and to keep on the road, and how to do the everyday sums that safe, sensible motoring depends on. This module covers the costs of motoring, from the standing costs you pay whether or not you drive, to the running costs that grow with every mile, and the smart ways to keep both down. It also covers the key calculations: how far a car travels on its fuel, the average speed of a journey, and the stopping distance, which is the thinking distance plus the braking distance. None of the maths is hard, but getting it right saves money and, on the road, can save far more than that.

Words for motoring costs

Learn these terms before the calculations are matched up. They name the ideas used in motoring costs and sums.

Match each calculation to what it finds

Standing costs against running costs

Motoring costs split into two main kinds, and telling them apart helps a driver plan a budget.

Which drawback comes with credit?

A driver pays for a car in monthly instalments through a finance deal instead of all at once. What is the main drawback?

• It usually costs more overall once interest is added
• It is against the law
• You never actually own the car
• It is always cheaper than paying cash

Cash against credit when buying

There is more than one way to pay for a car, and the choice changes the true cost. Paying with ready cash is simplest and adds nothing extra, but it ties up a large sum at once. Buying on credit, through a loan or a finance deal, spreads the cost into monthly payments, which is easier to manage but usually costs more overall once interest is added. The size of that interest is shown as the annual percentage rate, so a lower rate means a cheaper deal. Before signing anything, work out the total you will pay, not just the monthly figure, because a low monthly payment stretched over many years can hide a high final cost.

Pick the ways to cut motoring costs

Select every sensible way a driver can reduce the cost of motoring.

• Driving smoothly to use less fuel
• Shopping around for cheaper insurance
• Keeping up with servicing to avoid big repairs
• Driving as fast as possible everywhere
• Ignoring small faults until they grow

Order how to work out fuel consumption

Put the steps of working out a car fuel consumption in miles per gallon into a sensible order.

• Note the miles travelled since the last fill
• Note the gallons of fuel used
• Divide the miles by the gallons
• Read off the miles per gallon
• Compare it with the usual figure

Complete the motoring facts

Costs you pay whether or not you drive, such as road tax and insurance, are called _____ costs. Costs that depend on how much you drive, such as fuel and servicing, are called _____ costs. The value a car loses as it gets older is called _____. The total distance to pull up safely, made of thinking distance and braking distance, is the _____ distance.

Tap the two running costs

A driver lists four costs. Tap the TWO that are running costs, which grow the more you drive.

• the fuel you buy each week
• the servicing after every few thousand miles
• the yearly road tax
• the one-off driving licence fee

The price is the tip of the iceberg

The price on the windscreen is only the tip of the iceberg. Below the surface sit all the costs that keep coming after you have driven the car home: the tax, the insurance, the fuel, the servicing, the slow loss of value as the car ages, and the repairs that arrive when you least expect them. A cheap car with heavy costs beneath the waterline can end up dearer than a pricier one that sips fuel and holds its value. So a smart buyer looks past the sticker and adds up the whole iceberg, not just the part they can see above the water.

Work out the stopping distance

At a certain speed a car has a thinking distance of twelve metres and a braking distance of twenty-four metres. What is the total stopping distance in metres? Give the number only.

Make a smart motoring choice

Read each situation and choose the best answer.

• Two cars cost the same to buy, but one uses far less fuel. Which is likely cheaper to run?
• You want to lower your yearly motoring costs. What is a sensible step?
• The road is wet. What happens to your stopping distance?

Build a motoring-costs point

Choose the word for each gap to complete one point about the cost of motoring.

Explain the costs and calculations of motoring

A friend is about to buy their first car and asks what it will really cost to run and what sums they should know. Using what you have learned, explain the main points.

• Explain the difference between standing costs and running costs
• Explain what depreciation is
• Explain some sensible ways to reduce motoring costs
• Explain how to work out fuel consumption in miles per gallon
• Explain what a stopping distance is made up of