Question

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

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 km/hr and time of flight increased by 30 minutes. Find the duration of flight.

Answer 1

Let original speed of flight be x km/hr, then according to question,

`600/(x - 200) - 600/x = 30` minutes

⇒ `600 [1/(x - 200) - 1/x] = 30/60`   ...`[∵ "Time" = "Distance"/"Speed"]`

⇒ `(x - x + 200)/(x(x - 200)) = 1/(2 xx 600)`

⇒ `200/(x^2 - 200x) = 1/1200`

⇒ x² – 200x = 240000

⇒ x² – 200x – 240000 = 0

Here, a = 1, b = –200 and c = –240000

∴ `x = (200 +- sqrt(40000 + 960000))/(2  xx 1)`

= `(200 +- sqrt(1000000))/2`

= `(200 +- 1000)/2`

= `(200 + 1000)/2, (200 - 1000)/2`

= 600, – 400

Since, speed cannot be negative, therefore original speed = 600 km/hr and original distance = 600 km.

∴ Time = `"Original distance"/"Original speed"`

= `(600  km)/(600  km//hr)`

= 1 hr

Hence, the original duration of flight is 1 hr.