SOLUTION: Write a system of two equations in two variables to solve the problem. Flying with a tailwind, a pilot flew an airplane 720 miles in 4.5 hours. Flying into a headwind, the retur

Algebra ->  Equations -> SOLUTION: Write a system of two equations in two variables to solve the problem. Flying with a tailwind, a pilot flew an airplane 720 miles in 4.5 hours. Flying into a headwind, the retur      Log On


   

Question 868804: Write a system of two equations in two variables to solve the problem.
Flying with a tailwind, a pilot flew an airplane 720 miles in 4.5 hours. Flying into a headwind, the return trip took 6 hours. Find the speed of the plane in calm air 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 6 hours
with wind 4.5 hours

Distance against 720 miles distance with 720 miles
t=d/r against wind -
720.00 / ( x - y )= 6.00
6.00 ( x - y ) = 4.50
6.00 x - 6.00 y = 720.00 ....................1

720.00 / ( x + y )= 4.50
4.50 ( x + y ) = 720.00
4.50 x + 4.50 y = 720.00 ...............2
Multiply (1) by 4.50
Multiply (2) by 6.00
we get
27.00 x + -27.00 y = 3240.00
27.00 x + 27.00 y = 4320.00
54.00 x = 7560.00
/ 54.00
x = 140.00 mph

plug value of x in (1) y
6.00 x -6.00 y = 720.00
840.00 -6.00 -840.00 = 720.00
-6.00 y = 720.00
-6.00 y = -120.00 mph
y = 20.00
Plane speed 140.00 mph
wind speed 20.00 mph

m.ananth@hotmail.ca