# 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 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 /hour be the speed of the first train

Then the speed of the second train is (x - 5) km/hour

Given that they are 50 km apart after 2 hours

As per the given conditions

The first train travels from O to A and

The 2nd train travels from O to B

Also given that AB = 50 Km

Since the OAB is a right angled triangle

By Pythagoras theorem

OA2 + OB2 = AB2………….1

Now distance = speed × time

OA = x × 2

Also OB = 2(x - 5)

Putting value of OB and OA in 1

8 x2 – 40x + 100 = 2500

x2 – 5x – 300 = 0

x(x - 20) + 15(x - 20) = 0

(x + 15) (x - 20) = 0

x = - 15 or 20

Since speed cannot be negative the speed of the 1st train = 20 km/hour

And speed of 2nd train is 15 km/hour.

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