Question

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

Answer 1

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,

`"speed"="distance travelled"/"time taken to tavelled that distance"`

`x = d/t`

Or, d = xt (i)

Using the information given in the question, we obtain

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

(x + 1)(t - 2) = d

xt + 10t - 2x - 20 = d

By using equation (i), we obtain

−2x + 10t = 20 (ii)

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

(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.