SOLUTION: I have a question about one of my word problems. If you could help that would be great. How far west can a pilot go and return in a total time of 3 hours if his air speed is

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Question 58071: I have a question about one of my word problems. If you could help that would be great.

How far west can a pilot go and return in a total time of 3 hours if his air speed is 450 mph and the wind velocity from the west is 5 mph?

Any help with this would be great. Thanks.
Found 2 solutions by stanbon, hayek:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
How far west can a pilot go and return in a total time of 3 hours if his air speed is 450 mph and the wind velocity from the west is 5 mph?
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Let the distanc he can go be "x"
Going west DATA:
rate= 450-5 =445 mph ; distance = x miles ; time = d/r = x/445
----------------
Returning DATA:
rate = 450+5 = 455 mph; distance = x miles ; time = d/r = x/455
-----------------
EQUATIOn:
time west + time east = 3 hrs
x/445 + x/455 = 3
455x + 445x = 3*455*455
900x= 907425
x=674.92 miles (This is as far as he can go west)
Cheers,
Stan H.

Answer by hayek(51) (Show Source):
You can put this solution on YOUR website!
Using: Distance (d) = ground speed/rate (r) * time (t).
We know the pilot goes West for d miles, then east for d miles. The number of miles (d) in each direction is the same, because he returns to his starting point.
Therfore, lets break the problem into two pieces.
West:
d=?
r=450-5 (because the wind from the west will slow his ground speed)
t=
Eq. 1 ==>
East:
d=d
r=450+5 (because the wind will increase his ground speed going the other way)
t=
Eq.2 ==>
Finally, we know that the total time is three hours:
Eq. 3 ==>
We have three equations and three unknowns. Here's one way to solve them:
Eq 1 ==>
Eq 2 ==>
Plug those results into Eq. 3:

miles.