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The excursion boat on the river takes 2 hours to make the trip to a point 12 miles upstream and to return. If the rate at which the boat travels in still water is 5 times the rate of the river current, what is the rate of the current?

 Mar 9, 2020
 #1
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Let  the  current  rate = C

Then the rate  of the boat in still water = 5C

 

And   Distance  / Rate  = Time

 

The  effective rate withthe  current = 5C + C

 

The effective rate   against the current =  5C  -C

 

So

 

    12                   12

_______  +     ______   =     2 

(5C +C)           5C - C

 

 

    12                  12

   ____       +   ______  =  2

     6C                 4C

 

 

       2              6

     ___   +    ____  =    2

       C             C

 

 

           8

      _____  =    2                   multiply both sides  by  C

           C

 

 

          8  =   2C

 

          4  =   C    =  current rate in mph

 

     5C = 5 (4)   =  20  = boat rate in still water  in mph

 

 

 

cool cool cool

 Mar 10, 2020

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