Premium Online Home Tutors
3 Tutor System
Starting just at 265/hour

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.


Answer :

Ans.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 be d km.

Since Speed = Distance travelled/Time taken to travel the distance

=> \(x = {{d} \over {t}}\)
=> d = xt … (1)

According to the question
=> \(x + 10 = {{d} \over {t - 2}}\)
=>\((x + 10) (t - 2) = d\)
=> \(xt + 10t - 2x - 20 = d\)
=> \(-2x + 10t = 20\)……(2)[Using eq. (1)]
Again, => \(x - 10 = {{d} \over {t + 3}}\)
=>\((x - 10) (t + 3) = d\)
=> \(xt - 10t + 3x - 30 = d\)
=> \(3x - 10t = 30\)……(3)[Using eq. (1)]

Adding equations (2) and (3):
x = 50

Substituting the value of x in equation (2):
\((-2) (50) + 10t =20\)
\(=> –100 + 10t = 20\)
\(=> 10t = 120t\)
=> \(t = 12\)

From equation (1):
d = xt = (50)(12) = 600

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

NCERT solutions of related questions for Pair of linear equations in two variables

NCERT solutions of related chapters class 10 maths

NCERT solutions of related chapters class 10 science