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# 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.

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)]

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.