A plane left 30 minutes later than the scheduled time and in order to reach the destination, 1500km away in time. It has to increase the speed by 100km/h from the usual seed. Find the usual speed?

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/(2x 2 – x) = 1/6

⇒ 2x 2 – 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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