Question

A train covered a certain distance at a uniform speed. If the train could have been $10$ km/hr. faster, it would have taken $2$ hours less than the scheduled time. And, if the train were slower by $10$ km/hr; it would have taken $3$ hours more than the scheduled time. Find the distance covered by the train.

Answer 1

Let $t$ be the time taken by train and $s$ be the speed of the train.

The distance of the train is $st$.

If the train is 10 km per hour faster, then,

$\frac{st}{s+10}=t-2$

$10t-2s=20$ (1)

If the train is 10 km per hour slower, then,

$\frac{st}{s-10}=t+3$

$3s-10t=30$ (2)

From equation (1) and (2),

$s=50,t=12$

So the distance of the train is $50\times 12=600km$.