Question

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

Answer 1

Hey,

Given that  distance = 63 km.

Let original speed of train = x km/hr.

time = distance / time =  63/x hrs.

And it travels a distance of 72 kkm at a average speed of 6 km/hr more than the original speed.

distance = 72 km ; speed = (x + 6) km/hr .

time = 72/(x+6) hrs.

If it takes 3 hours to complete the whole journey

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

⇒ 63(x + 6) + 72x = 3x(x + 6)

⇒ 21(x + 6) + 24x = x(x+6)

⇒ 45x + 21×6 = x2 + 6x

⇒ x2 -  39x - 126 = 0

⇒ x2 - 39x - 126 = 0

⇒ (x - 42)(x + 3) = 0

∴ x = 42 km/hr

∴ the original average speed = 42 km/hr

HTH

:)