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Two trains are running on parallel rails and they travel at rate of $25$ and $30$ miles an hour. If the first train leaves an hour earlier than the second train, how much time will take for the second train to catch up with the first train?

Relative speed of the second train with respect to the first train $=30-25=5$ miles/hr

By the time second train start, first train is ahead by $25$ miles. Therefore, in $\dfrac{25}{5}=5\text{ hour,}$ second train will catch up with the first train.

Solution 2

Let required time be $t$ hour

By the time second train start, first train is ahead by $25$ miles. Therefore,

$25+25t=30t\\ \Rightarrow t=5$

Solution 3

Let required time be $t$ hour

Second train travels $t$ hours and first train travels $(t+1)$ hours. Since the distance travelled by both of the trains are same,