SOLUTION: A plane flew 720 miles in 3 hours with the wind. It would take 4 hours to travel the same distance against the wind. What is the rate of the plane in still air? What is the speed o

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Question 615280: A plane flew 720 miles in 3 hours with the wind. It would take 4 hours to travel the same distance against the wind. What is the rate of the plane in still air? What is the speed of the wind?
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 x-y 4 hours
with wind x+y 3 hours

Distance against wind 720 miles distance with wind 720 miles
t=d/r against wind
720 / ( x - y )= 4
4 ( x - y ) = 720
4 x - 4 y = 720 ....................1
with wind
720 / ( x + y )= 3
3 ( x + y ) = 720
3 x + 3 y = 720 ...............2
Multiply (1) by 3
Multiply (2) by 4
we get
12 x + -12 y = 2160
12 x + 12 y = 2880
24 x = 5040
/ 24
x = 210 mph

plug value of x in (1)
4 x -4 y = 720
840 -4 y = 720
-4 y = 720 -840
-4 y = -120
y = 30 mph
plane speed 210 mph
wind speed= 30 mph