Question

A train travels at a certain average speed for a distance of 132 km and then travels a distance of 140 km at an average speed of 4 km/h more than the initial speed. If it takes 4 hours to complete the whole journey, what was the initial average speed? Determine the time taken by train to cover the distances separately.

Answer 1

Distance = 132 km

Let the initial average speed of the train be x km/hr.

Distance = 140 km

The average speed to cover this distance = x + 4

Total time taken = 4hr

t = `D/S`

⇒ `132/x + 140/(x + 4) = 4`

⇒ `(132x + 528 + 140x)/(x(x+4)` = 4

⇒ 272x + 528 = 4x² + 16x

⇒ 4x² + 16x − 272x − 528 = 0

⇒ 4x² − 256x − 528 = 0

⇒ 4(x² − 64x − 132) = 0

⇒ x² − 64x − 132 = 0

⇒ x² − 66x + 2x − 132 = 0

⇒ x(x − 66) + 2(x − 66) = 0

⇒ (x − 66) (x + 2) = 0

⇒ x − 66 or x + 2 = 0

⇒ x = 66 or x ≠ 2

x = −2 is not admissible because it is negative.

Then, x = 66

Initial average speed of train = 66 km/hr

Time is taken to cover the distance separately as `132/66` and `140/70` i.e., 2 hours each.