Question

A plane left 30 minutes later than the scheduled time and in order to reach it's destination 1500 km away in time it has to increase it's speed by 250 km/h from it's usual speed . Find it's usual speed.

Answer 1

Sol: Let the usual time taken by the aeroplane = x km/hr Distance to the destination = 1500 km Case (i) Speed = Distance / Time = (1500 / x) Hrs   Case (iI)Time taken by the aeroplane = (x - 1/2) Hrs Distance to the destination = 1500 kmSpeed = Distance / Time = 1500 / (x - 1/2) Hrs   Increased speed = 250 km/hr   ⇒ [1500 / (x - 1/2)] - [1500 / x] = 250 ⇒ 1/(2x2 - x) = 1/6 ⇒ 2x2 - x = 6 ⇒ (x - 2)(2x + 3) = 0 ⇒ x = 2 or -3/2 Since, the time can not be negative, The usual time taken by the aeroplane = 2 hrs and the usual speed = (1500 / 2) = 750 km/hr.