Question

A train covered a certain distance at a uniform speed. If the train had been 10km/h faster , would have taken 2 hours less then the scheduled time .And if the train were slower by 10km/h , would have taken 3 hours more than the scheduled time . Find the distance covered by the train.

Answer 1

ans. 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



By using equation (i), we obtain

− 2x + 10t = 20 (ii)



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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