Question

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/hour more than its original speed. If it takes 3h to complete the total journey , then find its original average speed.
(Class 10 Maths Sample Question Paper)

Answer 1

Solution:

Let the original speed of train be x km/h and
The speed for the journey of 72 km will be (x +6) km/h.

ATQ

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

[ Time = Distance / speed]
3(21/x + 24 / x+6) = 3
(21/x + 24 / x+6) = 1
21(x+6)/x + 24(x) / x (x+6) = 1
21(x+6)/x + 24(x) = (1) x (x+6)
21x + 126 +24x = x² +6x
45x +126 = x² +6x
x² +6x - 45x -126 = 0
x² -39x -126= 0
x² -42x +3x -126= 0

[ By factorization method]
x (x-42) +3(x -42)= 0
(x+3)(x-42) = 0

x+3= 0
x = -3
x -42 = 0
x = 42

x cannot be negative because average speed of the train can't be negative.

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

HOPE THIS WILL HELP YOU....