A train travels at a certain average speed for a distance of 63 km and

1.	A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed?
Answer» Let its original average speed be x km/h. Therefore, 63/x + 72/(x + 6) = 3 7/x + 8/(x + 6) = 3/9 = 1/3 (7(x + 6) + 8x)/(x (x + 6)) = 1/3 i.e., 21 (x + 6) + 24x = x (x + 6) i.e., 21x + 126 + 24x = x² + 6x i.e., x² – 39x – 126 = 0 i.e., (x + 3) (x – 42) = 0 i.e., x = – 3 or x = 42 Since x is the average speed of the train, x cannot be negative. Therefore, x = 42. So, the original average speed of the train is 42 km/h.

A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed?

Answer»

Let its original average speed be x km/h. Therefore,

63/x + 72/(x + 6) = 3

7/x + 8/(x + 6) = 3/9 = 1/3

(7(x + 6) + 8x)/(x (x + 6)) = 1/3

i.e., 21 (x + 6) + 24x = x (x + 6)

i.e., 21x + 126 + 24x = x² + 6x

i.e., x² – 39x – 126 = 0

i.e., (x + 3) (x – 42) = 0

i.e., x = – 3 or x = 42

Since x is the average speed of the train, x cannot be negative.

Therefore, x = 42.

So, the original average speed of the train is 42 km/h.