A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.
Let the speed of the train be A km/hr and the time taken by the train to travel a distance be N hours and the distance to travel be X hours.
Speed of the train = Distance travelled by train / Time taken to travel that distance
A = N (distance)/ X (time)
Or, N = AX ..........(1)
Using the information that is given, we get:
(A+10) = X/(N-2)
(A + 10) (N – 2) = X
AN + 10N – 2A – 20 = X
By using the equation (1) we get,
– 2A + 10N = 20 .........(2)
(A-10) = X/(N+3)
(A – 10) (N + 3) = X
AN – 10N + 3A – 30 = X
By using the equation (1) we get,
3A – 10N = 30 ..........(3)
Adding equation (2) and equation (3) we get,
A = 50
Using the equation (2) we get,
(-2) x (50) + 10N = 20
-100 +10N = 20
=> 10N = 120
N = 12hours
From the equation (1) we get,
Distance travelled by the train, X = AN
= 50 x 12
= 600 km
Hence, the distance covered by the train is 600km.