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.
