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 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

− 2*x* + 10*t* = 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) + 10*t* = 20

−100 + 10*t* = 20

10*t* = 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.