Question 1197751
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In calm water, a motorboat can travel five times as fast as the current in the Amazon River. 
A trip upriver (upstream) and back totaling 96 km takes 5 hrs. Find the rate of the current.
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<pre>
Let x be the rate of the current in the river, in km/h.

Then the rate of the motorboat at calm water is 5x km/h;

the effective rate traveling downstream is 5x+x = 6x km/h;
the effective rate traveling   upstream is 5x-x = 4x km/h.


The total round trip is 96 km; hence, one way (each way) trip is 48 km.


Time equation is

    {{{48/(4x)}}} + {{{48/(6x)}}} = 5  hours.    (1)


Cancel common factors

    {{{12/x}}} + {{{8/x}}} = 5


Simplify and find x

    {{{20/x}}} = 5

     x = {{{20/5}}} = 4 km/h.


<U>ANSWER</U>.  The rate of the current is 4 km/h.


<U>CHECK</U>.  We will check equation (1):  {{{48/(4*4)}}} + {{{48/(6*4)}}} = {{{48/16}}} + {{{48/24}}} = 3 + 2 = 5 hours.   ! correct !
</pre>

Solved.