Question

Car A travels ‘x’ km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.

1. Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.
2. If car A uses 4 litres of petrol more than car B in covering 400 km. write down an equation, in A and solve it to determine the number of litres of petrol used by car B for the journey.

Answer 1

Let car A travel x km per litre and car B travel (x+5) km per litre.

Petrol used by car A: `400/x ` litres

Petrol used by car B: `400/(x+5)` litres

Given:

Car A uses 4 litres more petrol than car B.

`400/x = 400/(x+5) + 4`

Multiply both sides by x(x + 5):

400(x + 5) = 400x + 4x(x + 5)

400x + 2000 = 400x + 4x² + 20x

4x² + 20x − 2000 = 0

Divide by 4:

x² + 5x − 500 = 0

(x − 20) (x + 25) = 0

x = 20

Petrol used by car B = `400/(x+5)`

`=400/25`

= 16