A train covers a distance between two stations A and B in 45 minutes. If the speed of the train is reduced by 5 km/hr, then it covers the distance in 48 minutes. The distance between the stations A and B is :

Question: A train covers a distance between two stations A and B in 45 minutes. If the speed of the train is reduced by 5 km/hr, then it covers the distance in 48 minutes. The distance between the stations A and B is :

Solution:
Let
the distance between the stations A and B be x km
Time taken = 45 min = 45/60 = 3/4 hour

∴ Original speed =(x × 4/3)km/hr = 4x/3 km/hr

New speed = {(4x/3) - 5} km/hr.
= (4x - 15)/3 km/hr.

Now
x/{(4x - 15/3} =48/60
3x/(4x - 15) = 4/5
16x - 60 = 15x
16x - 15x = 60
x = 60 km