Q23 of 46 Page 1

A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If the takes 3 hours to complete the total journey, what is its first speed?

Let the average speed of train be x km/h.


Time taken by train to complete first 54 KM = t1 (in hours)



Speed after 54 km = (x + 6) km/h


Time taken by train to next 63 km/h = t2 (in hours)



Given


t1 + t2 = 3 hours




54x + 324 + 63x = 3x2 + 18x


3x2 - 99x + 324 = 0


x2 - 33x + 108 = 0


x2 - 36x + 3x - 108 = 0


x(x - 36) + 3(x - 36) = 0


x = 36 or x = - 3 [because in this case time(t1) will be negative, which is not possible]


So the average speed of train is 36 km/hr .


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