SOLUTION: Traveling for 3 hours into a steady headwind, a plane flies 1650 miles. The pilot determines that flying with the same wind for 2 hours, he could make a trip of 1300 miles. Find th

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Question 803697: Traveling for 3 hours into a steady headwind, a plane flies 1650 miles. The pilot determines that flying with the same wind for 2 hours, he could make a trip of 1300 miles. Find the speed of the plane and the speed of the wind?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Plane speed =x mph
wind speed =y mph
against wind 3 hours
with wind 2 hours

Distance against 1650 miles distance with 1300 miles
t=d/r against wind -
1650.00 / ( x - y )= 3.00
3.00 ( x - y ) = 2.00
3.00 x - 3.00 y = 1650.00 ....................1

1300.00 / ( x + y )= 2.00
2.00 ( x + y ) = 1300.00
2.00 x + 2.00 y = 1300.00 ...............2
Multiply (1) by 2.00
Multiply (2) by 3.00
we get
6.00 x + -6.00 y = 3300.00
6.00 x + 6.00 y = 3900.00
12.00 x = 7200.00
/ 12.00
x = 600.00 mph

plug value of x in (1) y
3.00 x -3.00 y = 1650.00
1800.00 -3.00 -1800.00 = 1650.00
-3.00 y = 1650.00
-3.00 y = -150.00 mph
y = 50.00
Plane speed 600.00 mph
wind speed 50.00 mph

m.ananth@hotmail.ca