Advertisement Remove all ads

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.

Advertisement Remove all ads

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.

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

NCERT Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.7 | Q 3 | Page 68
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×