The rate of consumption of petrol by a vehicle varies directly as the square of the distance covered. If 4 litres of petrol is consumed on a distance of 15km. how far would the vehicle go on 9 litres of petrol?

A.

22\(\frac{1}{2}\)km

B.

30km

C.

33\(\frac{1}{2}\)km

D.

45km

Correct answer is A

R \(\alpha\) D2

R = D2K

R = 4 Litres when D = 15cm

thus; 4 = 152k

4 = 225k

k = \(\frac{4}{225}\)

This gives R = \(\frac{4D^2}{225}\)

Where R = 9litres

equation gives

9 = \(\frac{4D^2}{225}\)

9 x 225 = 4d2

D2 = \(\frac{9 \times 225}{4}\)

D = \(\sqrt{9 \times 225}{4}\)

= \(\frac{3 \times 15}{2}\)

= 22\(\frac{1}{2}\)km