# 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 - Mathematics

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

− 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

= 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.

Concept: Equations Reducible to a Pair of Linear Equations in Two Variables
Is there an error in this question or solution?

#### APPEARS IN

NCERT Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.7 | Q 3 | Page 68