SOLUTION: Write a system of equations to model the problem and solve. Please show all work Theo flies from Atlanta to San Francisco. It takes 5.6 hours to travel 2100 miles against the hea

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Question 863896: Write a system of equations to model the problem and solve. Please show all work
Theo flies from Atlanta to San Francisco. It takes 5.6 hours to travel 2100 miles against the head wind. At the same time, Della flies from San Francisco to Atlanta. Her plane travels with the same avergae air speed. but with the tail wind. it only takes her 4.8 hours. Find the air speed and the wind speed.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Plane speed =x mph (both speeds are same)
wind speed =y mph
against wind 5.6 hours
with wind 4 hours

Distance against 2100 miles distance with 2100 miles
t=d/r against wind -
2100.00 / ( x - y )= 5.60
5.60 ( x - y ) = 4.00
5.60 x - 5.60 y = 2100.00 ....................1

2100.00 / ( x + y )= 4.00
4.00 ( x + y ) = 2100.00
4.00 x + 4.00 y = 2100.00 ...............2
Multiply (1) by 4.00
Multiply (2) by 5.60
we get
22.40 x + -22.40 y = 8400.00
22.40 x + 22.40 y = 11760.00
44.80 x = 20160.00
/ 44.80
x = 450.00 mph

plug value of x in (1) y
5.60 x -5.60 y = 2100.00
2520.00 -5.60 -2520.00 = 2100.00
-5.60 y = 2100.00
-5.60 y = -420.00 mph
y = 75.00
Plane speed 450.00 mph
wind speed 75.00 mph

m.ananth@hotmail.ca