SOLUTION: A pilot can travel 200 miles with the wind in the same amount of time as 150 miles against the wind Find the rate with and against the wind, the time with and against the wind and

Algebra ->  Rational-functions -> SOLUTION: A pilot can travel 200 miles with the wind in the same amount of time as 150 miles against the wind Find the rate with and against the wind, the time with and against the wind and       Log On


   

Question 1176137: A pilot can travel 200 miles with the wind in the same amount of time as 150 miles against the wind Find the rate with and against the wind, the time with and against the wind and how fast the pilot can travel in still air
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A pilot can travel 200 miles with the wind in the same amount of time as 150 miles against the wind
Find the rate with and against the wind, the time with and against the wind and how fast the pilot can travel in still air
:
let s = aircraft speed in still air
let w = rate of the wind
:
Write a time = dist/speed, establish a relationship between a/c speed and wind
:
200%2F%28%28s%2Bw%29%29 = 150%2F%28%28s-w%29%29
Cross multiply
200(s-w) = 150(s+w)
simplify, divide both sides by 50
4(s-w) = 3(s+w)
4s - 4w = 3s + 3w
4s - 3s = 3w + 4w
s = 7w
We know the s is a multiple of 7
Assume w = 30, then s = 210 mph is the speed of the a/c in still air
:
See if that works, find the times, should be equal
200%2F%28210%2B30%29%29%29 =
200%2F%28240%29 = .8333 hrs or .8333(60) = 50 min
and
150%2F%28%28210-30%29%29 =
150%2F%28180%29 = .83333 hrs or 50 min also
:
There are several possible integer solutions
Assume w=40 mph then s=280
that calculates to .625 hrs each way
or
Assume w=20 mph then s=140
that calculates to 1.25 hr each way