SOLUTION: Against the wind a commercial airline in South America flew 480 miles in 3 hours. With a tailwind the return trip took 2.5 hours. What was the speed of the plane in still air? What

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Question 981209: Against the wind a commercial airline in South America flew 480 miles in 3 hours. With a tailwind the return trip took 2.5 hours. What was the speed of the plane in still air? What was the speed of the wind?
Found 3 solutions by josgarithmetic, MathTherapy, Alan3354:
Answer by josgarithmetic(39625) About Me  (Show Source):
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r, speed if no wind
w, speed of the wind
Uniform Travel Rates Rule, RT=D to relate rate, time, distance


__________________speed________time________distance
AGAINST____________(r-w)________3___________480
WITHWND____________(r+w)________2.5_________480


system%28%28r-w%29%2A3=480%2C%28r%2Bw%29%282.5%29=480%29

system%283r-3w=480%2C2.5r%2Br.5w=480%29

Divide members of the first equation by 3, and divide members of the second equation by 2.5.
system%28r-w=160%2Cr%2Bw=192%29
Use elimination method to get both r and w.

Answer by MathTherapy(10555) About Me  (Show Source):
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Numbers_Word_Problems/981209: Against the wind a commercial airline in South America flew 480 miles in 3 hours. With a tailwind the return trip took 2.5 hours. What was the speed of the plane in still air? What was the speed of the wind?
1 solutions
Let speed of plane be S, and wind, TTravelling against wind, we get: S+-+T+=+480%2F3_____S+-+T+=+160 ------ eq (i)

Travelling with wind, we get: S+%2B+T+=+480%2F2.5_____S+%2B+T+=+192 -------- eq (ii)

2S = 352 ------- Adding eqs (ii) & (i)   

S, or plane's speed = 352%2F2, or highlight_green%28176%29

176 - T = 160 ------- Subbing 176 for S in eq (i)

- T = 160 - 176

- T = - 16

T, or speed of wind = %28-+16%29%2F%28-+1%29, or highlight_green%2816%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Against the wind a commercial airline in South America flew 480 miles in 3 hours. With a tailwind the return trip took 2.5 hours. What was the speed of the plane in still air? What was the speed of the wind?
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Find the 2 groundspeeds, upwind and downwind.
The plane's airspeed is the average of the 2.
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Windspeed is the difference between groundspeed and airspeed.