Question 37145
<pre><font size = 4><b>Problem: 
Jim can run 5 miles per hour on level ground on a still day. 
One windy day, he runs 10 miles with the wind, and in the same 
amount of time runs 4 miles against the wind. What is the rate 
of the wind?

Make this chart

               DISTANCE      RATE       TIME
With wind                                      
Against wind 

>>...he runs 10 miles with the wind, and in the same amount of time 
runs 4 miles against the wind...<<

Fill in the two distances                                  

               DISTANCE      RATE       TIME
With wind         10                            
Against wind       4                           

Let the rate of the wind be x miles per hour. 

So when running with the wind, his rate is increased by x mph.
So we add x to his rate of 5mph and get 5+x mph, so fill that
rate in: 

               DISTANCE      RATE       TIME
With wind         10         5+x      
Against wind       4        

When running against the wind, his rate is decreased by x mph.
So we subtract x from his rate of 5mph and get 5-x mph, so fill 
that rate in: 

               DISTANCE      RATE       TIME
With wind         10         5+x      
Against wind       4         5-x

Now use TIME = DISTANCE/RATE to fill in the two times:


               DISTANCE      RATE       TIME
With wind         10         5+x      10/(5+x)
Against wind       4         5-x       4/(5-x)


>>>...in the same amount of time...<<

This says the two times are equal:

               10      4
             ————— = —————
              5+x     5-x  

Multiply thru by LCD = (5+x)(5-x)

           10(5-x) = 4(5+x)

          50 - 10x = 20 + 4x

              -14x = -30

                 x = (-30)/(-14)

                 x = 15/7 or 2 1/7 mph

Checking:

When he runs with the wind he runs 5 + 2 1/7 mph or 7 1/7 mph 
or 50/7 mph for 10 miles.  Since T = D/R, his time is 10/(50/7)
= 7/5 hours

When he runs against the wind he runs 5 - 2 1/7 mph or 2 6/7 mph
or 20/7 mph for 4 miles.  Since T = D/R, his time is 4/(20/7)
= 7/5 hours

So the times are equal, thus the answer is correct.

Edwin
AnlytcPhil@aol.com</pre>