Question

An aeroplane left 30 mins later than its scheduled time and in order to reach its destination 1500 km away in time ,it had to increase its speed by 250 km/hr from its usual speed . Determine its usual speed.

Answer 1

its usual speed is 750kmlhr

Answer 2

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 km Speed = 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.

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