**Question: Two similar car models have fuel consumption as shown. You buy the diesel model which costs £500 more than the petrol model. You do 7000 miles per year on the motorway and 3000 urban miles. If diesel costs £5.38/gal, 35p more than petrol, how long does it take to recover the extra cost of the car?**

The essence of this question is that you buy a more expensive car which is more economical on fuel; how long will it take you to recover the extra cost? This is the type of problem that crops up in real life all the time. How do we go about solving it?

We need to break the problem down into discrete parts. We have to calculate the cost of motoring in the petrol car then the cost of motoring in the diesel car. The difference between them is the saving made each year in the diesel car. We then calculate how many years it will take for this saving to become greater than the difference in the price of the cars.

**Step 1. The cost of motoring in the petrol car**

The amount of fuel used is the distance travelled divided by the economy (mpg) of the car. For the petrol car this is:

The cost of petrol is £5.38-0.35=£5.03 per gallon which gives a total annual cost of 254.9*5.03=£1282.15.

**Step 2. The cost of motoring for the diesel car**

For the diesel car the number of gallons required for the same mileage is:

The diesel fuel is more expensive at £5.38 but with the lower number of gallons used the total is 185.9*£5.38=£1000.14.

**Step 3. Calculate the saving and the time required**

The saving per year is £1282.15-£1000.14=£282.01. So, given that the car cost £500 more to purchase, it will take:

This may be the answer required or you may have to convert this into years and months or weeks or days depending on how the answers are formatted. If, for instance, the answer was stated in years and weeks then take the decimal part of the answer (0.773) and multiply it by 52 (weeks in a year) to get 40 (approximately) and the answer would then be 1year 40weeks.