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 x km/h and the time taken by train to travel the given distance be t hours and the distance to travel was d km.

We know that,




Or, d = xt (i)


Using the information given in the question, we obtain


(x+10) =


(x+10) (t-2) = d


Xt+10t-2x-20 = d


By using equation (i),


we obtain - 2x + 10t = 20 (ii)


(x-10) =


(x-10) (t+3) = d


Xt-10t+3x-30 = d


By using equation (i), we obtain 3x - 10t = 30 (iii)


Adding equations (ii) and (iii),


we obtain x = 50


Using equation (ii), we obtain ( - 2) × (50) + 10t = 20


- 100 + 10t = 20 10t = 120


t = 12 hours


From equation (i), we obtain


Distance to travel = d = xt


= 50 × 12


= 600 km


Hence, the distance covered by the train is 600 km.


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