When there is decrease of 5 km/hr in the usual uniform speed of train, it takes 4 hrs. more than the usual time for covering the distance of 400 km. Find the usual speed of the train.

Worlded
probelm solving

Let X be the time taken when train is moving in its normal speed.

Y be the normal speed of the train.

Speed = distance/time

that is X = 400 / Y

or Y = 400 / X --------- (1)

When speed is decreased by 5 km/hr time increases by 4 hour

that is X + 4 = 400 / Y -5

= X + 4 = 400 X / 400 - 5X ( substitute Y = 400 /X we get this equation)


on solving we get 5X^2 + 20x - 1600 = 0

we get two solutions X = 16 and -20

-20 is neglected (time cannot be negative)

substitute X in equation (1)

Y = 400 / 16 = 25 km/hr

So normal speed of train is 25 km/hr.