Question

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 ?​

Answer 1

Answer:

Step-by-step explanation:

Solution :-

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

Time taken to cover 63 km = 63/x hr

New speed = (x + 6) km/hr

Time taken to cover 72 km = 72/(x + 6) hr

According to the Question,

⇒ 63/x + 72/(x + 6) = 3

⇒ 21/x + 24/(x + 6) = 1

⇒ (21x + 126 + 24x) = x(x + 6)

⇒ 45x + 126 = x² + 6x

⇒ x² - 39x - 126 = 0

⇒ x² - 42x + 3x - 126 = 0

⇒ x(x - 42) + 3(x - 42) = 0

⇒ (x + 3)(x - 42) = 0

⇒ x = - 3, 42 (As x can't be negative)

⇒ x = 42

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