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.

Question

Philoid · Accepted Answer

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.