SOLUTION: An airplane took 4 hours to fly 2400 miles against a head wind. the return trip with the wind took 3 hours. What is the speed of the plane in still air and the speed oof the wind?

Question 771159: An airplane took 4 hours to fly 2400 miles against a head wind. the return trip with the wind took 3 hours. What is the speed of the plane in still air and the speed oof the wind?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Plane speed =x mph
wind speed =y mph
against wind 4 hours
with wind 3 hours

Distance with wind 2400 miles distance against wind 2400
t=d/r against wind (x-y)
2400.00 / ( x - y )= 4.00

4.00 x - -4.00 y = 2400.00 ....................1
with wind (x+y)
2400.00 / ( x + y )= 3.00
3.00 ( x + y ) = 2400.00
3.00 x + 3.00 y = 2400.00 ...............2
Multiply (1) by 3.00
Multiply (2) by 4.00
we get
12.00 x + -12.00 y = 7200.00
12.00 x + 12.00 y = 9600.00
24.00 x = 16800.00
/ 24.00
x = 700 mph

plug value of x in (1) y
4 x -4 y = 2400
2800 -4 -2800 = 2400
-4 y = 2400
-4 y = -400 mph
y = 100
Plane 700 mph
wind 100 mph

CHECK
x+y= 800
X-y= 600 +
2400.00 / ( 800.00 )= 3
2400 / ( 600 ) = 4

RELATED QUESTIONS
an airplane took 2 hours to fly 600km against a head wind. the return trip with the wind... (answered by longjonsilver)

An airplane took 2 hours to fly 600 km against a head wind. The return trip with the... (answered by Paul)

An airplane took 2 hours to fly 600 km against a head wind. The return trip with the wind (answered by Alan3354)

An airplane took 2 hours to fly 600 km against a head wind. The return trip with the wind (answered by josmiceli)

An airplane took 3 hours to fly 1800 miles against a headwind. The return trip with the... (answered by lwsshak3)

An airplane took 2 hours to fly 600 km against head wind. The return trip with the wind... (answered by checkley77)

[ It took an airplane 3 hours to fly 1260 mi against a headwind. The return trip with the (answered by TimothyLamb)

An airplane took 4 hours to fly 1200 miles agianst a headwind.The return trip with the... (answered by mananth,MathTherapy,Alan3354)

An airplane took 3hrs to fly 1800 miles against a headwind. The return trip with the wind (answered by Alan3354)