(Q11)Two trains leave a railway station at the same time.The first train travels towards west and the second train towards north. The first train travels 5km/hr faster than the second train. If after two hours they are 50km. apart, find the average speed of each train.

Answer:

Let the speed of the slower train = x kmph

Then speed of the faster train = x + 5 kmph.

NorthStarting pointWest50(x+5)x22(x)

Distance = speed × Time

Distance travelled by the first train = 2(x + 5) = 2x + 10

Distance travelled by the second train = 2.x = 2x

By the Pythagoras Theorem

(hypotenuse)2 = (side)2 + (side)2

(2x)2 + (2x + 10)22 = 502

4x2 + (4x2 + 40x + 100) = 2500

4x2 + 4x2 + 40x + 100 = 2500

8x2 +40x - 2400 = 0

x2 + 5x - 300 = 0

x2 +20x - x - 300 = 0

x(x + 20) - x(x + 20) = 0

(x + 20)(x-) = 0

x - = 0 or x + 20 = 0

x = (or) -20

But x cant be negative.

∴ Speed of the slower train x = kmph

∴ Speed of the faster train x + 5 = + 5 = kmph