SOLUTION: a plane can fly 4800km in 4h with the wind. the return trip against the same wind takes 5h. find the rate of the plane in the still air and the rate of the wind. please shows steps

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Question 703514: a plane can fly 4800km in 4h with the wind. the return trip against the same wind takes 5h. find the rate of the plane in the still air and the rate of the wind. please shows steps thank you
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
Plane speed =x mph
wind speed =y mph
against wind 5 hours
with wind 4 hours

Distance with wind 4800 miles distance against wind 4800
t=d/r against wind (x-y)
4800.00 / ( x - y )= 5.00

5.00 x - -5.00 y = 4800.00 ....................1
with wind (x+y)
4800.00 / ( x + y )= 4.00
4.00 ( x + y ) = 4800.00
4.00 x + 4.00 y = 4800.00 ...............2
Multiply (1) by 4.00
Multiply (2) by 5.00
we get 2.00
20.00 x + -20.00 y = 19200.00
20.00 x + 20.00 y = 24000.00
40.00 x = 43200.00
/ 40.00
x = 1080 mph

plug value of x in (1) y
5 x -5 y = 4800
5400 -5 -5400 = 4800
-5 y = 4800
-5 y = -600 mph
y = 120
Plane 1080 mph
wind 120 mph

CHECK
x+y= 1200
X-y= 960 +
4800.00 / ( 1200.00 )= 4
4800 / ( 960 ) = 5