# Determine the speed of an airplane?

An airplane makes a 990 km flight with a trailwind and returns, flying into the same wind. The total flying time is 3 hours 20 minutes, and the airplane's sped in still air is 600 km/h What is the speed of the wind?

Update:

An airplane makes a 990 km flight with a tailwind and returns, flying into the same wind. The total flying time is 3 hours 20 minutes, and the airplane's speed in still air is 600 km/h. What is the speed of the wind?

Relevance

Let v = speed of wind

speed of plane on the first part of the trip = 600 + v

speed of plane on the return trip = 600 - v

time for the first part of the trip = distance/speed = 990/( 600 + v)

time for the second part of the trip = 990 / (600 - v)

total time for the round trip is

990/( 600 + v) + 990 / (600 - v)

but this has to equal 3 hrs 20 min = 3 1/3 hrs = 10/3 hrs

990/( 600 + v) + 990 / (600 - v) = 10/3

99/( 600 + v) + 99 / (600 - v) = 1/3

1/( 600 + v) + 1 / (600 - v) = 1/ [ (99)(3) ]

(600 - v)/ {(600+v)(600 - v)} + (600 +v) / {(600 +v)(600 - v} = 1/297

1200/ { ( 600 + v)(600 - v) } = 1/297

(600 + v)( 600 - v) / 1200 = 297

(600 + v) ( 600 -v) = (297)(1200)

600^2 - v^2 = 356400

v^2 = 600^2 - 356400 = 3600

v = 60 km/hr

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