Question

In a flight of 600 km, an aircraft was slowed down due to bad weather. The average speed of the trip was reduced by 200 kmph and the time of flight increased by 30 minutes. Find the duration of the flight.

Answer 1

Given: Distance = 600 km.

Speed reduced by 200 km/h causes time to increase by 30 minutes (0.5 h).

Let the original speed = x km/h.

Step-wise calculation:

1. Original time = `600/x` hours. 

New time = `600/(x - 200)` hours.

2. Increase in time:

`600/(x - 200) - 600/x = 0.5`

3. Multiply out:

`(600x - 600(x - 200))/(x(x − 200)) = 0.5` 

⇒ `120000/(x^2 - 200x) = 0.5`

4. Rearrange:

x² – 200x – 240000 = 0

5. Factor:

(x – 600)(x + 400) = 0 

⇒ x = 600   ...(Reject x = –400)

6. Duration = `600/600`

= 1 hour

The duration of the flight (original) is 1 hour.