Question 1204447
<pre>
She did it by adding the two distances they rode together to equal
the total distance of 25 miles.

Another way is the approach rate method.  That method is to add the 
two rates and that gives the rate at which the distance between them 
is shrinking to zero. That is, the total 25 miles distance between 
them reduces to zero when they come together. 

Their approach rate is the sum of their rates, so
If the faster rate is x, the slower rate is (2/3)x.
Their approach rate is the sum of their rates, x+(2/3)x or (5/3)x.

They pass each other is 2 hours.  The distance between them is 25 miles.

Since (rate)(time) = distance,
       [(5/3)x](2) = 25 
           (10/3)x = 25
               10x = 75
                 x = 7 1/2 mph = rate of faster biker.
            
                 (2/3)x = (2/3)(7 1/2) = (15/2)(2/3) = 5 mph = rate of slower
biker.

Edwin</pre>