SOLUTION: A plane left an airport and flew with the wind for 3 hours, covering 1200 miles. It then returned over the same route to the airport against the wind in 4 hours. Find the rate of t

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Question 539550: A plane left an airport and flew with the wind for 3 hours, covering 1200 miles. It then returned over the same route to the airport against the wind in 4 hours. Find the rate of the plane in still air and the speed of the wind.
write steps please! thanks.
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
Plane speed =x mph
Wind speed =y mph
against wind x-y 4.00 hours
with wind x+y 3.00 hours

Distance = same= 1200 miles
t=d/r
1200 / ( x - y )= 4.00
4 ( x - y ) = 1,200.00
4 x -4 y = 1200 ....................1
1200 / ( x + y )= 3.00
3.00 ( x + y ) = 1200
3.00 x + 3.00 y = 1200 ...............2
Multiply (1) by 3.00
Multiply (2) by 4.00
we get
12 x + -12 y = 3600
12 x + 12 y = 4800
24 x = 8400
/ 24
x = 350 mph

plug value of x in (1)
4 x -4 y = 1200
1400 -4 y = 1200
-4 y = 1200 -1400
-4 y = -200
y = 50 mph
Plane 350 mph
Wind 50 mph
m.ananth@hotmail.ca