Question

A plane can fly 1120km in 1 hour 20 minutes with the wind. Flying against the same wind, the plane travels the same distance in 1 hour 24 minutes. Find the speed of the plane and the speed of the wind.

Answer 1

Here,

Let the speed of the plane in still air = x km/h,

And the speed of the wind = y km/h,

Then,

With the wind (downstream speed) = (x + y) km/h,

Against the wind (upstream speed) = (x − y) km/h,

According to the given condition, forming equations,

Distance = 1120 km

(1) With the wind: Time = 1 hr 20 min = `4/3` hr

`1120/(x + y) = 4/3`

`x + y = (1120 xx 3)/4`

x + y = 840     ...(i)

(2) Against the wind: Time = 1 hr 24 min = `7/5` hr

`1120/(x - y) = 7/5`

`x - y = (1120 xx 5)/7`

x − y = 800     ...(ii)

Now, adding equation (ii) and (i):

(x + y) + (x − y) = 840 + 800

x + y + x − y = 1640

2x = 1640

x = `1640/2`

∴ x = 820

Substitute x = 820 into equation (i):

820 + y = 840

y = 840 − 820

∴ y = 20

Hence, the Speed of the plane in still air is 820 km/h, and the Speed of the wind is 20 km/h.