Question

An aeroplane left 50 minutes later than its scheduled time, and in order to reach the destination, 1250 km away, in time, it had to increase its speed by 250 km / hr from its usual speed. Find its usual speed.

Answer 1

The usual speed of an aeroplane is 500 km/hr.

Given,

The distance covered by the aeroplane = 1250 km

Let the usual speed be = x km/hr

Time taken by the plane with usual speed = 1250 / x

Speed of the aeroplane after increasing the speed = (x+250) km/hr

Time taken by the plane with increased speed = 1250 / (x+250)

From given data, we have,

$\dfrac{1250}{x} - \dfrac{1250}{x+250} = 50$

1250 [ 1/x - 1/(x+250) ] = 50

1/x - 1/(x+250) = 1/25

solving the above equation, we get,

x^2 + 250x - 375000 = 0

x^2 + 750x - 500x - 375000 = 0

x (x+750) - 500 (x+750) = 0

(x+750) (x-500) = 0

x = -750, 500

Since, the speed cannot be a negative value, therefore x = 500

Therefore, the usual speed of the aeroplane = 500 km/hr