Question 442300
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A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back
took 70 hours. What is the speed of the boat in still water? What is the speed of the current?
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        The solution by @mananth has too much excessive calculations,

        which means that his computer code, which produces his text and calculations,

        is badly organized and creates  anti-pedagigic narrative.

        As a result,  the solution by @mananth scares readers and is a bad way to teach.


        Below is my solution,  which is a standard treatment of the problem without making unnecessary calculations.



<pre>
The effective speed downstream is

    {{{210/10}}} = 21 mph.


The effective speed upstream is

    {{{210/70}}} = 3 mph.


If u  is the rate of the boat at no current and v is the rate of current, then

    u + v = 21    (1)

    u - v =  3    (2)


By adding equations, you get  2u = 21 + 3 = 24,  u = 24/2 = 12 mph.

Bu subtracting eq.(2) from eq.(1), you get  2v = 21 - 3 = 18,  v = 18/2 = 9 mph.


<U>ANSWER</U>.  The rate of the boat at no current is 12 mph.

         The rate of the current is 9 mph.
</pre>

Solved in the most straightforward form and in the most educative way, without making excessive calculations.