Question

In a flight of 6000 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 400 km/h and time increased by 30 minutes. Find the original duration of flight.

Answer 1

Let the original speed of the aircraft be x km/h.

Distance = 6000 km

Original time = `6000/x` hours

Reduced speed = x − 400 km/h

New time = `6000/(x-400)` hours

Given that the time increased by 30 minutes = 0.5 hours:

`6000/(x-400)`

`= 6000/x + 0.5`

Multiply both sides by x(x − 400):

6000x = 6000x − 2,400,000 + 0.5x² − 200x

0 = 0.5x² − 200x − 2,400,000

Multiply by 2:

x² − 400x − 4,800,000 = 0

(x − 2400) (x + 2000) = 0

x = 2400 or x = −2000

Original time = `6000/2400 = 2.5` hours

The original duration of the flight was:

2.5 hours