Question

Car A travels x km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
(i) Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.
(ii) 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

Distance travelled by car A in one litre = x km
and distance travelled by car B in one litre = (x + 5) km
(i) Consumption of car A in covering 400 km

 = `(400)/x` litres and consumption of car B

= `(400)/(x + 5)`litres
(ii) According to the conditions,

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

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

⇒ `(400 xx 5)/(x^2 + 5x)` = 4

⇒ 2000 = 4x² + 20x
⇒ 4x² + 20x – 2000 = 0
⇒ x² + 5x – 500 = 0  ...(Dividing by 2)
⇒ x² + 25x – 20x - 500 = 0
⇒ x(x + 25) – 20(x + 25) = 0
⇒ (x + 25)(x – 20) = 0
Either x + 25 = 0,
then x = –25,
but it is not possible as it is im negative.
or
x - 20 = 0,
then x = 20
∴ Petrol used by car B = 20 - 4 = 16 litres.