Question 1189181
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Two kayakers paddle 18 km downstream with the current in the same time it takes them to go 8 km upstream against the current. 
The rate of the current is 3 km/hr. What is the rate of the kayakers in still water?
Fill in the details:
Downstream: Distance (km)? Rate (km/hr)? Time (hr)
Upstream: Distance (km)? Rate (km/hr)? Time (hr)
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<pre>
Let x be the rate of the kayakers in still water.


Then the rate paddling downstream is (x+3) km/h; time paddling downstream is  {{{18/(x+3)}}} hours.

     the rate paddling   upstream is (x-3) km/h; time paddling   upstream is  {{{18/(x-3)}}} hours.


The times are the same, giving this time equation


    {{{18/(x+3)}}} = {{{8/(x-3)}}}.


Solve by cross-multiplying


    18*(x-3) = 8*(x+3)

    18x - 54 = 8x + 24

    18x - 8x = 24 + 54

       10x   =   78

         x   =  78/10 = 7.8 km/h


<U>ANSWER</U>.  The rate of kayakers in still water is  7.8 km/h.


<U>CHECK</U>.  The time paddling downstream is  {{{18/(7.8+3)}}} = {{{18/10.8}}} hours = {{{180/108}}} = {{{10/6}}} hours = 100 minutes.

        The time paddling   upstream is  {{{8/(7.8-3)}}} = {{{8/4.8}}} = {{{80/48}}} hours = {{{10/6}}}  hours = 100 minutes.   ! Correct ! 
</pre>

Solved and explained.