The distance between Delhi and Agra is 200 km. A train travels the first 100 km at a speed of 50 km/h. How fast must the train travel the next 100 km. so as to average 70 km/h for the whole journey ?

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Solution

Total distance $= 200 k m$
Average speed $= 70 k m / h$
Total time taken $= \frac{Total dostance}{Average speed} = \frac{200}{70} = \frac{20}{7} h$
For first part of the journey,
Distance $= 100 k m$
$S p e e d$ = 50\ km/h$
Time taken, $t_{1} = \frac{100}{50} = 2 h$
For second part of the journey,
Distance $= 100 k m$
Speed $= x k m / h$
Time taken, $t_{2} = \frac{100}{x} h$
$t_{1} + t_{2} = \frac{20}{7}$
$2 + \frac{100}{x} = \frac{20}{7}$
$\frac{100}{x} = \frac{6}{7}$
$700 = 6 x$
$\Rightarrow x = 116.6 k m / h$

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