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Question:

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.

Solution:

Let the speed of the train be x km/h and the time taken by train to travel the given distance be t hours and the distance to travel be d km. We know that,
⇒Speed=Distance/Time
⇒x=d/t
∴d=xt.. (i)
Case 1
⇒(x+10)×(t-2)=d
⇒xt+10t-2x-20=d
⇒d+10t-2x-20=d
⇒-2x+10t=20.. (ii)
Case 2
⇒(x-10)×(t+3)=d
⇒xt-10t+3x-30=d
⇒d-10t+3x-30=d
⇒3x-10t=30. (iii)
Adding equations (ii) and (iii), we get
⇒x=50
Substitute the value of x in (ii) we get
⇒(-2)×(50)+10t=20
⇒-100+10t=20
⇒10t=120
⇒t=12 hours
Substitute the value of t and x in equation (i), we get
Distance to travel=d=xt
⇒d=12×50=600Km
Hence, the distance covered by the train is 600km.