SOLUTION: Patricia flew a small airplane for 3 hours with the wind and traveled 585km. The return trip against the wind took 5 hours. Find the rate at which she flew in still air. What

Question 689652: Patricia flew a small airplane for 3 hours with the wind and traveled 585km. The return trip against the wind took 5 hours. Find the rate at which she flew in still air.

What I have tried and failed:
3(r+w)=585 --> 3r+3w=585
5(r-w)=585 --> 5r-5w=585
15r+15w=2925 15r=8775
15r-15w=1755 r=585 3(585)+3w=585
1755+3w=585
-1755 -1755 <--- I figured this was wrong
because it was negative..

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a small airplane for 3 hours with the wind and traveled 585km.
The return trip against the wind took 5 hours.
Find the rate in still air
:
Let's do it this way
:
Write a distance equation for each way
3(r+w) = 585
5(r-w) = 585
:
Simplify, divide the 1st equation by 3, divide the 2nd equation by 5, results:
r + w = 195
r - w = 117
-------------addition eliminates w, find r
2r = 312
r = 312/2
r = 156 km/h in still air
:
:
You can confirm this, find w and check in the original equations
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