Question

An airplane flies against the wind from A to B in 8 hours. The same airplane returns from B to A, in the same direction as the wind, in 7 hours. Find the ratio of the speed of the airplane (in still air) to the speed of the wind. 

Answer 1

Let x = speed of airplane in still air, y = speed of wind and D the distance between A and B. Find the ratio x / y 

Against the wind: D = 8(x - y), with the wind: D = 7(x + y) 

8x - 8y = 7x + 7y, hence x / y = 15

Answer 2

solution:-

Let's assume that the speed of airplane in still air be Vp

And the speed of air be Vw

The distance between A and B is d

When the airplane is moving against the direction of wind the relative speed will be

Vr = Vp -Vw

And when the airplane is moving in the direction of wind the relative speed will be

Vr = Vp + Vw

Now in the first case time taken is 8 hr while in the second case it is 7 hr. Therefore we can write

d/(Vp -Vw) = 8

d/(Vp +Vw) = 7

[d/(Vp -Vw)]/[d/(Vp +Vw)] = 8/7

(Vp + Vw)/(Vp -Vw) = 8/7

(Vp +Vw)/(Vp - Vw) +1 = 8/7 +1

2Vp/(Vp -Vw) = 15/7

(Vp -Vw)/2Vp = 7/15

(Vp - Vw)/ Vp = 14/15

1 - Vw/ Vp = 14/15

Vw / Vp = 1 -14/15 =1/15

Vw/Vp = 1/15 Ans

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