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WAEC Mathematics 2015 Paper

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Question : 36

Total: 45

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?

22 $\frac{1}{2}$ km
30km
33 $\frac{1}{2}$ km
45km

Solution:

Concept:

Petrol consumption

R

varies directly as the square of distance

D

, so

R = kD^2

.

Explanation:

Given

R = 4

litres when

D = 15

km.

Substitute into

R = kD^2

:

4 = k(15)^2

4 = 225k

k = \frac{4}{225}

So the relation is

R = \frac{4D^2}{225}

.

Now put

R = 9

litres:

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

9 \times 225 = 4D^2

D^2 = \frac{9 \times 225}{4}

D = \sqrt{\frac{9 \times 225}{4}}

D = \frac{3 \times 15}{2}

D = \frac{45}{2} = 22\frac{1}{2}

km.

Answer:

A.

22\frac{1}{2}

km

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