Question

In a flight of 600 km, an aircraft was slowed due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of the flight increased by 30 minutes. Find the scheduled duration of the flight.

Answer 1

Let the normal Speed of the aircraft be S, and time taken be t.

Distance = 600 km 

Time = `"Distance"/"Speed"` 

Hence , t = `600/S` ......(i)

And t + 0.5 = `600/(S - 200)` ......(ii)

Puttiing (i) in (ii), we get 

`600/(S - 200) - 1/2 = 600/S`

⇒ `(1200 - S + 200)/(2  S - 400) = 600/"S"`

⇒ 1200 S – S² + 200 S = 1200 S – 2400000 

⇒ S² – 200 S – 240000 = 0 

⇒  S² – 600 S + 400 S – 240000 = 0

⇒ S (S – 600) + 400 (S – 600) = 0 

⇒ (S – 600) (S + 400) = 0 

Hence, S = 600 km/hr 

⇒ T = `600/600` = 1 Hour