A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6 km/hr more than its original speed. If it takes 3 hours to complete total journey, what is the original average speed?
Let original speed of the train be x km/h.
Time taken to travel 63 km = 63/x hours
New speed = (x + 6) km/hr
Time taken to travel 72 km = 72/(x + 6) hours
According to the question,
63/x + 72/(x + 6) = 3
x2 - 39x - 126 = 0
(x - 42)(x + 3) = 0
x = -3 or x = 42
As the speed cannot be negative, x = 42
Thus, the average speed of the train is 42 km/hr.