waecmaths question:
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
Option A:
$22\tfrac{1}{2}km$
Option B:
30km
Option C:
$33\tfrac{3}{4}km$
Option D:
$45km$
waecmaths solution:
$\begin{align} & R\propto {{d}^{2}} \\ & R=k{{d}^{2}} \\ & 4=k{{(15)}^{2}} \\ & k=\frac{4}{225} \\ & \text{When }R=9 \\ & 9=\frac{4}{225}{{d}^{2}} \\ & {{d}^{2}}=\frac{9\times 225}{4} \\ & d=\sqrt{\frac{9\times 225}{4}}=\frac{3\times 15}{2}=22.5 \\\end{align}$
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