Question

volvia nation of example

Answer 1

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.