SOLUTION: Flying with the wind, a small plane flew 280 mi in 2 h. Against the wind, the plane could fly only 170 mi in the same amount of time. Find the rate of the plane in calm air and the
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Question 868814: Flying with the wind, a small plane flew 280 mi in 2 h. Against the wind, the plane could fly only 170 mi in the same amount of time. Find the rate of the plane in calm air and the rate of the wind. Answer by mananth(16946) (Show Source):
Distance against 170 miles distance with 280 miles
t=d/r against wind -
170.00 / ( x - y )= 2.00
2.00 ( x - y ) = 2.00
2.00 x - 2.00 y = 170.00 ....................1
280.00 / ( x + y )= 2.00
2.00 ( x + y ) = 280.00
2.00 x + 2.00 y = 280.00 ...............2
Multiply (1) by 1.00
Multiply (2) by 1.00
we get
2.00 x + -2.00 y = 170.00
2.00 x + 2.00 y = 280.00
4.00 x = 450.00
/ 4.00
x = 112.50 mph
plug value of x in (1) y
2.00 x -2.00 y = 170.00
225.00 -2.00 -225.00 = 170.00
-2.00 y = 170.00
-2.00 y = -55.00 mph
y = 27.50
Plane speed 112.50 mph
wind speed 27.50 mph
