Question 733604
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a boatman goes 96 km in 8 hours with the flow of a river and returns in 12 hours (against the flow). 
what will be the respective speed of the boat and the river (in km/hour)?
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<pre>
Let u be the speed of the boat at no current (in kilometers per hour),
and let v be the rate of the current.


The speed of the boat with    the current is  96/8 = 12 km/h.

The speed of the boat against the current is  96/12 = 8 km/h.


The speed of the boat with    the current is  (u + v)  km/h.

The speed of the boat against the current is  (u - v)  km/h.


So, we have these equations

    u + v = 12,    (1)

    u - v =  8.    (2)


By adding equations (1) and (2),               we get  2u = 12 + 8 = 20;  hence,  u = 20/2 = 10 km/h.

By subtracting equation (2) from equation (1), we get  2v = 12 - 8 =  4;  hence,  v = 4/2 = 2 km/h.


<U>ANSWER</U>.  The speed of the boat at no current is 10km/h.

         The rate of the current is 2 km/h.
</pre>

Solved.


The answers in the post by @lynnlo are incorrect.