Question 74234
<pre>
A motor boat can run 25 mph in still water. The boat starts at 7:00 am going upstream in a river whose current runs at 5 mph. How far up the river can the boat go and still be back at 12:00 noon? 


What is asked in the problem?
    How far up the river can the boat go and still be back at 12:00noon?

Given:
Rate of motor boat in still water is 25mph
Rate of the current is 5mph
Time ranges from 7:00am to 12:00noon. That's is 5 hours difference.

Representation:
Let x be the distance the boat travel up or down
    y = the time it takes the boat to travel upstream
  5 - y = the time it takes the boat to travel downstream


                rate     *      time          =       distance
Upstream       25 - 5             y           =         x

Downstream     25 + 5           5 - y         =         x


                      (25 - 5)y = x      eq1
                  (25 + 5)(5-y) = x      eq2

Solve using substitution method

                   20y = x
                30( 5 - y) = x
                150 - 30y = 20y
                 150 = 50y
                   3h = y  this is the time it takes the boat to 
                           travel upstream

               5 - y = 5 - 3
                     = 2 hours --> this is the time it takes the boat to 
                                   travel downstream
   when y = 3

               20y = x
               20(3) = x
                 60m = x  This is the distance travel either upstream 
                          or downstream