A train travels from A to B for 30 km at a uniform speed of 30 kmph. Its average speed after traveling another 40 km from B to C is 45 kmph for the whole journey. What was the average speed of the train from B to C?

70 kmph

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72 kmph

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75 kmph

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90 kmph

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Solution

The correct option is B 72 kmph
First part of journey:
Speed, $v_{1} = 30 k m / h$
Distance, $s_{1} = 30 k m$
Time taken is:
$t_{1} = \frac{s_{1}}{v_{1}}$
$t_{1} = \frac{30 k m}{30 k m / h}$
$t_{1} = 1 h$

Second part of journey:
Distance, $s_{2} = 40 k m$
Let the speed be $v_{2}$ and time taken be $t_{2}$
$s_{2} = v_{2} t_{2}$
$v_{2} t_{2} = 40 k m$

Full journey:
Total distance travelled:
$d = d_{1} + d_{2}$
$d = 30 k m + 40 k m$
$d = 70 k m$
Total time taken:
$t = t_{1} + t_{2}$
$t = 1 + t_{2}$
Average speed:
$v = \frac{d}{t}$
$45 = \frac{70}{1 + t_{2}}$
$t_{2} = \frac{25}{45} h$

But $v_{2} t_{2} = 40 k m$
$v_{2} \times \frac{25}{45} h = 40 k m$
$v_{2} = 72 k m / h$

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