SOLUTION: A turboprop plane flying with the wind flew 960 mi in 3 h. Flying against the wind, the plane required 4 h to travel the same distance. Find the rate of the wind and the rate of th
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Question 908100: A turboprop plane flying with the wind flew 960 mi in 3 h. Flying against the wind, the plane required 4 h to travel the same distance. Find the rate of the wind and the rate of the plane in calm air. Answer by mananth(16946) (Show Source):
Distance against 960 miles distance with 960 miles
t=d/r against wind -
960.00 / ( x - y )= 4.00
4.00 ( x - y ) = 3.00
4.00 x - 4.00 y = 960.00 ....................1
960.00 / ( x + y )= 3.00
3.00 ( x + y ) = 960.00
3.00 x + 3.00 y = 960.00 ...............2
Multiply (1) by 3.00
Multiply (2) by 4.00
we get
12.00 x + -12.00 y = 2880.00
12.00 x + 12.00 y = 3840.00
24.00 x = 6720.00
/ 24.00
x = 280.00 mph
plug value of x in (1) y
4.00 x -4.00 y = 960.00
1120.00 -4.00 -1120.00 = 960.00
-4.00 y = 960.00
-4.00 y = -160.00 mph
y = 40.00
plane speed 280.00 mph
wind speed 40.00 mph
