<PRE><B>Question 83758</B>
Jim can run 5 miles per hour on level ground on a still day. One windy day, he runs 13 miles with the wind, and in the same amount of time runs 5 miles against the wind. What is the rate of the wind?
:
Let x = speed of the wind
Then:
(5+x) = speed with the wind:
(5-x) = speed against the wind:
:
It says the time for the two situations is the same; write a time equation
Time = Dist/speed
:
time against  = time with
{{{5/((5-x))}}} =  {{{13/((5+x))}}} 
:
Cross multiply:
5(5+x) = 13(5-x)
:
25 + 5x = 65 - 13x 
5x + 13x = 65 - 25
18x = 40
x = 40/18
x = 2.22 mph is the speed of the wind; 
:
:
Check solutions; see if the times are equal:
Speed with: 5 + 2.22 = 7.22; Speed against: 5 - 2.22 = 2.78
13/7.22 = 1.8 hrs
5/2.78  = 1.8 hrs</PRE>