Question 73

Find the length of a train, if it completely crosses two bridges of lengths 600 m and 300 m in 80 seconds and 60 seconds, respectively.

Solution

Let's assume the length of a train is 'y'.

As we know that the speed of the train is the same in both cases.

$$\frac{length\ of\ train\ +length\ of\ first\ bridge}{time}\ =\ \frac{length\ of\ train\ +length\ of\ second\ bridge}{time}$$

$$\frac{y+600}{80}\ =\ \frac{y\ +300}{60}$$

$$\frac{y+600}{4}\ =\ \frac{y\ +300}{3}$$

3y+1800 = 4y+1200

4y-3y = 1800-1200

y = 600

Length of a train = 600 m

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