SOLUTION: Against the wind a small plane flew 210 miles in 1 hour and 10 minutes. The return trip took only 50 minutes. What was the speed of the wind? What was the speed of the plane is sti

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Question 782682: Against the wind a small plane flew 210 miles in 1 hour and 10 minutes. The return trip took only 50 minutes. What was the speed of the wind? What was the speed of the plane is still air?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Plane speed =x mph
wind speed =y mph
against wind 1 1/6 hours
with wind 5/6 hours

Distance against 210 miles distance with 210 miles
t=d/r against wind -
210.00 / ( x - y )= 1.17
1.17 ( x - y ) = 0.83
1.17 x - 1.17 y = 210.00 ....................1

210.00 / ( x + y )= 0.83
0.83 ( x + y ) = 210.00
0.83 x + 0.83 y = 210.00 ...............2
Multiply (1) by 0.83
Multiply (2) by 1.17
we get
0.97 x + -0.97 y = 175.00
0.97 x + 0.97 y = 245.00
1.94 x = 420.00
/ 1.94
x = 216 mph

plug value of x in (1) y
1.17 x -1.17 y = 210.00
252.00 -1.17 -252.00 = 210.00
-1.17 y = 210.00
-1.17 y = -42.00 mph
y = 36
Plane speed 216 mph
wind speed 36 mph