# 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 us assume, the uniform speed of the train be x km/h and the time is taken to travel a given distance be t hours. Then distance can be calculated by;

distance = speed × time

Let the uniform speed of the train be distance be t hours

Then the distance be xt km

x km/h and the scheduled time to travel the given

When the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time;

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

xt - 2x + 10t - 20 = xt

-2x + 10t = 20 ....(1)

When the train were slower by10 km/h, it would have taken 2 hours

more than the scheduled time;

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

xt + 3x - 10t - 30 = xt

3x -10t = 30 ....(2)

Adding equations (1) and (2), we obtain

x = 50

Substituting x = 50 in equation (1), we obtain

-2 × 50 +10t = 20

-100 + 10t = 20

10t = 120

t = 120/10

t = 12

Therefore, distance,

xt = 50 × 12 = 600

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

**Video Solution:**

## 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

### Class 10 Maths NCERT Solutions - Chapter 3 Exercise 3.7 Question 3:

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

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. Then the distance covered by the train is 600 km