#### Question

If the speed of an aeroplane is reduced by 40 km/hr, it takes 20 minutes more to cover 1200 km. Find the speed of the aeroplane.

#### Solution

Let the original speed of the aeroplane be x km/hr.

Time taken to cover a distance of 1200 km = 1200/x hrs

`("Time" = "Distance"/"Speed")`

Let the new speed of the aeroplane be (x - 40) km/hr

Time taken to cover a distance of 1200 km = `1200/(x - 40)` hrs

From the given information we have

`1200/(x - 40) - 20/60 = 1200/x`

`1200/(x - 40) - 1200/x = 20/60`

`(1200x - 1200x + 48000)/(x(x - 40)) = 1/3`

x(x - 40) = 48000 x 3

`x^2 - 40x - 144000 = 0`

`x^2 - 400x + 360x - 144000 = 0`

x(x - 400) + 360(x - 400) = 0

(x - 400)(x + 360) = 0

x = 400,-360

But, speed cannot be negative. So, x = 400.

Thus, the original speed of the aeroplane is 400 km/hr.