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 the actual speed of the train be and the actual time taken by y hours. Then,

Distance covered=

If the speed is increased by, then time of journey is reduced by 2 hours

when speed is , time of journey is

Distance covered=

When the speed is reduced by, then the time of journey is increased by when speed is, time of journey is

Distance covered=

Thus, we obtain the following system of equations:

By using cross multiplication, we have

Putting the values of x and y in equation (i), we obtain

Distance=

Hence, the length of the journey is .