Question 767121
a boat traveling at a constant speed goes 45 miles with the current, then turns around and travels for 50 miles against the current. if the speed of the current is 5 mph and the total time for the trip was 4 hours, find the speed of the boat on calm water
<pre>
Let x = speed in calm water,
Then his speed with the current = x+5
And his speed against the current = x-5
Let t = time with current
then his time against the current = 4-t 

Make this DRT chart:

                  distance  |  speed  |  time = {{{distance/speed}}}
   with current     45      |  (x+5)  |      {{{45/(x+5)}}} 
against corrent     50      |  (x-5)· |      {{{50/(x-5)}}}



        The equation comes from:

                {{{(matrix(6,1,

TIME,BOAT,TRAVELED,WITH,THE,CURRENT))}}}{{{""+""}}}{{{(matrix(6,1,

TIME,BOAT,TRAVELED,AGAINST,THE,CURRENT))}}}{{{""=""}}}{{{(matrix(3,1,

TOTAL,TIME,TRAVELED))}}}

                          {{{45/(x+5)}}}{{{""+""}}}{{{50/(x-5)}}}{{{""=""}}}{{{4}}}

Multiply through by LCD of (x+5)(x-5)

                 45(x-5) + 50(x+5) = 4(x+5)(x-5)

             45x - 225 + 50x + 250 = 4(x²-25)
                          95x + 25 = 4x² - 100

Get 0 on the left side:

                                 0 = 4x² - 95x - 125
                                 0 = (x-25)(4x+5)

                               x-25=0     4x+5=0
                                  x=25     4x=-5
                                            x={{{-5/4}}}
    
Ignore the negative answer.

Answer = 25 mph

Edwin</pre>