SOLUTION: An airplane makes the 1800 mile trip from Boston to Houston in 6 hours and makes the return trip in 4.5 hours. Assuming that the plane travels at a constant airspeed and the wind b
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Question 863515: An airplane makes the 1800 mile trip from Boston to Houston in 6 hours and makes the return trip in 4.5 hours. Assuming that the plane travels at a constant airspeed and the wind blows at a constant rate from west to east, find (a) the plane's airspeed and (b) the wind speed. Answer by mananth(16946) (Show Source):
Distance against 1800 miles distance with 1800 miles
t=d/r against wind -
1800.00 / ( x - y )= 6.00
6.00 ( x - y ) = 4.50
6.00 x - 6.00 y = 1800.00 ....................1
1800.00 / ( x + y )= 4.50
4.50 ( x + y ) = 1800.00
4.50 x + 4.50 y = 1800.00 ...............2
Multiply (1) by 4.50
Multiply (2) by 6.00
we get
27.00 x + -27.00 y = 8100.00
27.00 x + 27.00 y = 10800.00
54.00 x = 18900.00
/ 54.00
x = 350.00 mph
plug value of x in (1) y
6.00 x -6.00 y = 1800.00
2100.00 -6.00 -2100.00 = 1800.00
-6.00 y = 1800.00
-6.00 y = -300.00 mph
y = 50.00
Plane speed 350.00 mph
current speed 50.00 mph
