SOLUTION: With the wind, a plane flew 1780 miles in 6 hours. On the return trip, the pilot was forced to land after 2 hours, having traveled only 440 miles. Find the rate of the plane in sti

Question 579243: With the wind, a plane flew 1780 miles in 6 hours. On the return trip, the pilot was forced to land after 2 hours, having traveled only 440 miles. Find the rate of the plane in still air and the rate of the wind.
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 2 hours
with wind x+y 6 hours

Distance = 1780 miles distance= 440
t=d/r against wind
440.00 / ( x - y )= 2.00

2.00 x - -2.00 y = 440.00 ....................1

1780.00 / ( x + y )= 6.00
6.00 ( x + y ) = 1780.00
6.00 x + 6.00 y = 1780.00 ...............2
Multiply (1) by 3.00
Multiply (2) by 1.00
we get
6.00 x + -6.00 y = 1320.00
6.00 x + 6.00 y = 1780.00
12.00 x = 3100.00
/ 12.00
x = 258.33 mph

plug value of x in (1)
2 x -2 y = 440
516.67 -2 y = 440
-2 y = 440 -516.67
-2 y = -76.67
y = 38.33 mph
Plane speed = 258.33 mph
wind speed = 38.33 mph
m.ananth@hotmail.ca

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