In this page quadratic equation practical solution10 we are going to see solution of practice question of the worksheet quadratic equation practical application.

Question 10:

Two trains leave railway stations at the same time. The first train travels due west and the second train due north. The first 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.

Solution:

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

So sped of first train will be (x + 5) km/hr

Distance covered by the 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 + 2 (2x) (10) ] + 4x 2 = 2500

8 x² + 40 x + 100 – 2500 = 0

8 x² + 40 x – 2400 = 0

Now we are going to divide the whole equation by 8

x² + 5 x – 300 = 0

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

x + 20 = 0       x – 15 = 0

x = -20            x = 15

Therefore speed of the second train is 15 km/hr

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