Question

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

Answer 1

Let the usual time taken by the aeroplane = x km/hr

Distance to the destination = 1500km

We know that,

Given that speed has to increase by 250 km/hr

⇒ 6(2x – 2x + 1) = 2x² – x

⇒ 6 = 2x² – x

⇒ 2x² –x – 6 = 0

⇒ 2x² – 4x + 3x – 6 = 0

⇒ 2x (x – 2) + 3 (x – 2) = 0

⇒ (2x + 3) (x – 2) = 0

⇒ (2x + 3) = 0 or (x – 2) = 0

∴ x = 3/2 or x = 2

Since, time can’t be negative.

Hence, the time taken by the aeroplane is 2hrs and the speed is 750km/hr