SOLUTION: A plane flies 1500 miles against the wind in 3 hours and 45 minutes. The return trip with the wind takes 3 hours. Assume that the wind speed stays constant. Find the speed of the w

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Question 436704: A plane flies 1500 miles against the wind in 3 hours and 45 minutes. The return trip with the wind takes 3 hours. Assume that the wind speed stays constant. Find the speed of the wind and the speed of the airplane with no wind.
Answer by mananth(16946) About Me  (Show Source):
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A plane flies 1500 miles against the wind in 3 hours and 45 minutes. The return trip with the wind takes 3 hours. Assume that the wind speed stays constant. Find the speed of the wind and the speed of the airplane with
no wind.
against wind 3.75 hours
with wind 3.00 hours

Distance = same= 1500
plane speed =x
wind speed =y
t=d/r
1500/(x-y)=3.75
3.75(x-y)=1,500.00
3.75x -3.75y=1500 ....................1
1500/(x +y)=3.00
3.00(x+y)=1500
3.00x+3.00y= 1500 ...............2
Multiply (1) by 9.88
Multiply (2) by 13.00
we get
37.05x-37.05y=14820
39x+39y=19500
76.05x= 34320
/76.05
x=451.28 mph plane speed

plug value of x in (1)
3.75 x-3.75y =1500
1692.31 -3.75y= 1500
-3.75y=1500-1692.31
-3.75y=-192.31
y=51.28 mph wind speed