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Apr 28, 2014

# A plane left 30 min later than the scheduled time and in order to reach the destination 1500km away in time it has to increase the speed by 250km/h from the usual speed. find its usual speed

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

Ramesh

Member since Apr 1, 2014

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 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.

Syeda

Member since Jan 25, 2017

Answer, 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. SME Approved
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