Q8 of 58 Page 108

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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