Question

Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels 5 km/hr faster than the second train. If after 2 hours, they are 50 km apart, find the speed of each train.

Answer 1

Let take the speed of the second train to be x km/hr

Then, the speed of the first train is (x + 5) km/hr

Let O be the position of the railway station from which the two trains leave.

Distance travelled by the first train in 2 hours 

= OA

= Speed × Time

= 2(x + 5) km

Distance travelled by the second train in 2 hours

= OB

= Speed × Time

= 2x km

By Pythagoras Theorem, we have

(AB)² = (OA)² + (OB)²

`=>` (50)² = [2(x + 5)]² + (2x)²

`=>` 2500 = 4(x + 5)² = 4x²

`=>` 2500 = 4(x² + 25 + 10x) + 4x²

`=>` 8x² + 40x – 2400 = 0

`=>` x² + 20x – 15x – 300 = 0

`=>` (x + 20)(x – 15) = 0

`=>` x = –20 or x = 15

`=>` x = 15   ...[∵ x cannot be negative]

Hence, the speed of the second train is 15 km/hr and the speed of the first train is 20 km/hr.