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.

Answer 1

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 × 3

x² – 40x – 144000 = 0

x² – 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.