Question

An aeroplane takes 3 hours to fly 1200 km against the wind. The return trip takes 2 hours. Find the speed of the plane in still air and the wind speed.

Answer 1

Here, let x = speed of the plane in still air (km/h),

And y = speed of the wind (km/h)

Using formula: `"Speed" = "Distance"/"Time"`

According to the given condition,

(1) Against the wind:

Speed of plane = x − y km/h

Time taken = 3 hours

Distance = 1200 km

`x - y = 1200/3`

x − y = 400     ...(i)

(2) With the wind (return trip):

Speed of plane = x + y km/h

Time taken = 2 hours

Distance = 1200 km

`x + y = 1200/2`

x + y = 600     ...(ii)

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

(x − y) + (x + y) = 400 + 600

x − y + x + y = 1000

2x = 1000

x = `1000/2`

∴ x = 500

Substitute x = 500 in equation (i),

500 − y = 400

∴ y = 100

Hence, the Speed of the plane in still air is 500 km/h, and the Speed of the wind is 100 km/h.