SOLUTION: the speed of an airplane in still air is 257 mph. the plane travels 570 mi against the wind and 1780 with the wind in a total time of 9 hr. what is the speed of the wind?

Question 82147: the speed of an airplane in still air is 257 mph. the plane travels 570 mi against the wind and 1780 with the wind in a total time of 9 hr. what is the speed of the wind?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
the speed of an airplane in still air is 257 mph. the plane travels 570 mi against the wind and 1780 with the wind in a total time of 9 hr. what is the speed of the wind?
-----------
Against the wind DATA:
Distance = 570 mi ; Rate = 257-wind ; Time = d/r = 570/(257-w) hr.
----------
With the wind DATA:
Distance = 1780 mi ; Rate = 257+wind; Time = d/r = 1780/(257+w) hr.
---------------
EQUATION:
time with + time against = 9 hr.
1780/(257+w) + 570/(257-w) = 9
Multiply thru by (257^2-w^2) to get:
1780(257- w) + 570(257 + w) = 9(257^2-w^2)
603950 - 1210w = 594441 - 9w^2
9w^2-1210w+9509 = 0
w = [1210 +- sqrt(1210^2-4*9*9509)]/18
w = [1210+-1059.14]/18
Positive answer: w = 126.06 mph
===============
Cheers,
Stan H.

RELATED QUESTIONS
The speed of an airplane in still air is 243 mph. The plane travels 663 mi against the... (answered by ankor@dixie-net.com)

The speed of an airplane in still air is 248 mph. The plane travels 816 mi agains the... (answered by josmiceli)

The speed of an airplane in still air is 214mph. The plane travels 819mi against the wind (answered by checkley71,stanbon)

An airplane flies 1449 mi against the wind and 1539 mi with the wind in a total time of... (answered by josmiceli)

the speed of an airplane in still air is 153 mph. The plane travels 849 mph against the... (answered by ptaylor)

An airplane flies 738 mi against the wind and 1062 mi with the wind in a total time of 9... (answered by checkley77)

plane travels 470 mph with wind; 410 mph against the wind; speed in still... (answered by tmwilliamlin168)

the speed of an airplane in still air is 224km/h. the plane travels 716 km against the... (answered by ptaylor)

THE SPEED OF AN AIRPLANE IN STILL AIR IS 224KM/H. THE PLANE TRAVELS 733KM AGAINST THE... (answered by solver91311,josmiceli,ankor@dixie-net.com)