Question

The distance between two stations is $340$ km. Two trains start simultaneously from these stations on parallel tracks and cross each other. The speed of one of the them is greater than that of the other by $5$ km/hr. If the distance between two trains after $2$ hours of their start is $30$ km., find the speed of each train.

Answer 1

Let $r$ be the speed of first train.

And $r+5$ be the speed of other train.

The distance first train travels in $2$ hours is $=2r$

The distance other train travels in $2$ hours is $(r+5)\times 2=2(r+5)$

Now we know that the distance the first train travels $\left(2r\right)$ plus the distance the other train travels $2(r+5)$ equals $340-30=310$.

So, $2r+2(r+5)=310$

$\Rightarrow 2r+2r+10=310$

$\Rightarrow 4r=300$

$\Rightarrow r=75$

Thus, speed of first train is $75$ mph.

Therefore, the speed of other train is $r+5=75+5=80$ mph.