Q. 324.8( 13 Votes )

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.

Answer :

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


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