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Two athletes cover the same distance at the speed of 30 kmph and 32 kmphs respectively. Find the distance travelled by them if one takes 15 minutes longer than the other.

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120 km

150 km

160 km

200 km

answer is A.

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Detailed Solution

Total distance = x km

Time to complete the distance with 32 kmph = t hrs

$\frac{x}{32} = t, \frac{x}{30} = t + \frac{15}{60}$

$\frac{x}{30} = \frac{x}{32} + \frac{15}{60}$

$\frac{x}{30} - \frac{x}{32} = \frac{1}{4}$

$\frac{16 x - 15 x}{480} = \frac{1}{4}$

$\frac{x}{120} = 1$

$x = 120 k m$

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