SOLUTION: 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 to

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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
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
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
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%2Fspeed
   with current     45      |  (x+5)  |      45%2F%28x%2B5%29 
against corrent     50      |  (x-5)· |      50%2F%28x-5%29



        The equation comes from:

                %28matrix%286%2C1%2C%0D%0A%0D%0ATIME%2CBOAT%2CTRAVELED%2CWITH%2CTHE%2CCURRENT%29%29%22%22%2B%22%22%28matrix%286%2C1%2C%0D%0A%0D%0ATIME%2CBOAT%2CTRAVELED%2CAGAINST%2CTHE%2CCURRENT%29%29%22%22=%22%22%28matrix%283%2C1%2C%0D%0A%0D%0ATOTAL%2CTIME%2CTRAVELED%29%29

                          45%2F%28x%2B5%29%22%22%2B%22%2250%2F%28x-5%29%22%22=%22%224

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%2F4
    
Ignore the negative answer.

Answer = 25 mph

Edwin