SOLUTION: A plane can travel 400 miles against the wind in the same time that it can travel 500 miles with the wind. If the speed of wind was 10 miles per hour. Find the speed of the plane i

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A plane can travel 400 miles against the wind in the same time that it can travel 500 miles with the wind. If the speed of wind was 10 miles per hour. Find the speed of the plane i      Log On


   

Question 150817: A plane can travel 400 miles against the wind in the same time that it can travel 500 miles with the wind. If the speed of wind was 10 miles per hour. Find the speed of the plane in still air.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Windspeed = w
w+=+10+mi%2Fhr
p = speed of plane is still air
t = time flying against and with the wind
Against the wind:
(1) 400+=+%28p+-+10%29%2At
With the wind:
(2) 500+=+%28p+%2B+10%29%2At
Multiply both sides of (1) by 5
Multiply both sides of (2) by 4
2000+=+5%2A%28p+-+10%29%2At
and
2000+=+4%2A%28p+%2B+10%29%2At
Since they both equal 2000, make them equal to eachother
5%2A%28p+-+10%29%2At+=+4%2A%28p+%2B+10%29%2At
Divide both sides by t
5%2A%28p+-+10%29+=+4%2A%28p+%2B+10%29
5p+-+50+=+4p+%2B+40
p+=+90 mi/hr
The speed of the plane in still air is 90 mi/hr
check:
(1) 400+=+%28p+-+10%29%2At
(1) 400+=+%2890+-+10%29%2At
400+=+80t
t+=+5 hrs
and
(2) 500+=+%28p+%2B+10%29%2At
(2) 500+=+%2890+%2B+10%29%2At
500+=+100t
t+=+5 hrs
OK