Question 1200510
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A motorboat can maintain a constant speed of 34 miles per hour relative to the water. 
The boat makes a trip upstream to a certain point in 35 ​minutes; 
the return trip takes 33 minutes. What is the speed of the​ current?
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Let "c" be the speed of the current, in miles per hour.


Then the rate of the boat moving upstream   is (34-c) miles per hour;

     the rate of the boat moving downstream is (34+c) miles per hour.


The distance of both trips is the same, so we write the distance equation

    {{{(34-c)*(35/60)}}} = {{{(34+c)*(33/60)}}}.


Multiply both sides by 60 and simplify

    (34-c)*35     = (34+c)*33

    34*35 - 35c   = 34*33 + 33c

    34*35 - 34*33 = 33c + 35c

      34*(35-33)  =    68c

         34*2     =    68c

           c      =    {{{(34*2)/68}}} = {{{68/68}}} = 1.


<U>ANSWER</U>.  The speed of the current is 1 mile per hour.
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Solved.