Question 286237: An airplane makes a 990 km flight with a tailwind and returns, flying into the same wind. The total flying time is 3 hours and 20 minutes, and the airplane's speed in still air is 600 km/h. What is the speed of the wind?
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! An airplane makes a 990 km flight with a tailwind and returns, flying into the same wind. The total flying time is 3 hours and 20 minutes, and the airplane's speed in still air is 600 km/h. What is the speed of the wind?
D distance = R rate * T time
air speed still air + tail wind speed = speed with tail wind
(or Vg1 = Va + Vw or 600 + Vw = Vg1)
air speed still air - tail wind speed = speed without tail wind
(or Vg2 = Va - Vw or 600 - Vw = Vg2)
T = T1 + T2 = 10/3 hrs
T2 = 10/3 - T1
990 = Vg1T1 = Vg2T2
Vw = Vg1 - 600
-Vw = Vg2 - 600 --> Vw = 600 - Vg2
Vg1 - 600 = 600 - Vg2
Vg1 + Vg2 = 1200
Vg2 = 1200 - Vg1
Vg1 * T1 = (1200 - Vg1)* (10/3 - T1)
Vg1T1 = 4000 - 1200T1 - (10/3)Vg1 + Vg1T1
0 = 4000 - 1200T1 - (10/3)Vg1
0 = 4000 - 1200(990/Vg1) - (10/3)Vg1
0 = 4000Vg1 - 1188000 - (10/3)Vg1^2
0 = 1200Vg1 - 356400 - Vg1^2
Vg1^2 - 1200Vg1 + 356400 = 0 (rearranged)
(Vg1 - 540)(Vg1 - 660) = 0
check with FOIL: Vg1^2 - 660Vg1 - 540Vg1 + 356400
Vg1 = 540 or 660
Vg1 > Vg2 therefore Vg1 is 660
Vg1 = 660 = Va + Vw = 600 + Vw --> Vw = 60
then: Vg2 = 540 = Va - Vw = 600 - Vw --> Vw = 60
check: 990 = 660 * T1, 990 = 540 * T2
1.5 hours = T1
990/540 = 99/54 = 33/18 = 11/6 hours = T2
T1 + T2 = 1.5 hours + 11/6 hours = 3/2 + 11/6 = 9/6 + 11/6 = 20/6 = 10/3 hours
T1 + T2 = 3 hours and 20 minutes
Wind Speed is 60 km/hr
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