Question 1177337
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A kayak can travel 24 miles downstream in 2 ​hours, while it would take 12 hours to make the same trip upstream. 
Find the speed of the kayak in still​ water, as well as the speed of the current. 
Let k represent the speed of the kayak in still​ water, and let c represent the speed of the current.
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Let k be the rate of the kayak in still water (in miles per hour)
and c be the rate of the current (in the same units).


Then the effective rate of the kayak downstream is k + c
and  the effective rate of the kayak   upstream is k - c.


From the problem, the effective rate of the kayak downstream is the distance of 24 miles 
divided by the time of 2 hours  {{{24/2}}} = 12 mph.

                  The effective rate of the plane upstream is the distance of 24 miles 
divided by the time of 12 hours  {{{24/12}}} = 2 mph.


So, we have two equations to find 'k' and 'c'

    k + c = 12,    (1)

    k - c =  2.    (2)


To solve, add equations (1) and (2).  The terms 'c' and '-c' will cancel each other, and you will get

    2k = 12 + 2 = 14  --->   k = 14/2 = 7.

Now from equation (1)

     v = 12 - u = 12 - 7 = 5.


<U>ANSWER</U>.  The rate of the kayak in still water is 7 mph.  The rate of the current is 5 mph km/h.
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Solved.