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 two hours, they are 50 km apart, find the average speed of each train.

Let x km/hr. be the speed of second train.

So, speed of first train will be (x + 15) km/hr.

Distance covered by first train in 2 hours = 2(x + 5)

Distance covered by the second train in 2 hours = 2x

By using Pythagoras theorem

[2(x + 5)]² + (2x)² = 50²

⇒ (2x + 10)² + (2x)² = 50²

⇒ (4x² + 100 + 40x) + 4x² = 2500

⇒ 8x² + 40x + 100 = 2500

⇒ 8x² + 40x + 100 –2500 = 0

⇒ 8x² + 40x – 2400 = 0

Divide by 8 both sides

⇒ x² + 5x – 300 = 0

⇒ x² + 20x – 15x – 300 = 0

⇒ x(x + 20) – 15 (x + 20) = 0

⇒ (x – 15)(x + 20) = 0

x – 15 = 0 or x + 20 = 0

x = 15 or x = –20

Therefore, speed of the second train is 15 km/hr.