A train covered a certain distance at a uniform speed. If the train had been 5 kmph faster, it would have taken 3 hours less than the scheduled time. And, if the train were slower by 4 kmph, it would have taken 3 hours more than the scheduled time. Find the length of the journey.
Let the speed of train be s kmph and the scheduled time be t hours
Also, Let the length of journey be d.
∴ s × t = d.....(1)
According to question -
(s + 5)(t - 3) = d
⇒ st - 3s + 5t - 15 = d
⇒ 3s - 5t = - 15.....(2) [ ∵ s × t = d from (1) ]
and,
(s - 4)(t + 3) = d
⇒ st + 3s - 4t - 12 = d
⇒ 3s - 4t = 12.....(3) [ ∵ s × t = d from (1) ]
Subtracting equation (2) from (3), we get -
t = 27
Substituting the value of t in equation (3), we get -
s = 40
∴ d = s × t = 40×27 = 1080 km
Thus, the length of the journey = 1080 Km