Question 1208621
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A boat travels 30 km/h in still water. If this boat goes upstream in a river flowing at a rate of 12 km/h, for 5 km, 
and returns back downstream to its starting point, what is the average speed for the whole trip in km/h?
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<pre>
The boat's own speed in still water  is 30 km/h.

The rate of the current in the river is 12 km/h.


So,  the boat' speed with the current (downstream)  is  u = 30 + 12 = 42 km/h;

     the boat' speed against the current (upstream) is   v = 30 - 12 = 18 km/h.


Now, if you know the theory, you may use the ready formula for the average speed of the two-ways trip


    {{{V[average]}}} = {{{(2u*v)/(u+v)}}} = {{{(2*42*18)/(42+18)}}} = {{{(2*42*18)/60}}} = {{{2*42*(3/10)}}} = 25.2 km/h.    <U>ANSWER</U>



        If you don't know this theory, 
        you may complete the solution in couple of steps.



The travel time upstream is   {{{5/18}}}  of an hour;  travel time downstream is  {{{5/42}}}  of an hour.


The average speed is  the total distance 5 + 5 = 10 km, divided by the total time  {{{5/18}}} + {{{5/42}}}  of an hour.


Thus the average speed is


    {{{10/(5/18+5/42)}}} = {{{10/(((5*42+5*18)/(18*42)))}}} = {{{(10*(18*42))/(5*42+5*18)}}} = {{{(2*18*42)/(42+18)}}} = the same formula and the seme result = 25.2 km/h.


<U>ANSWER</U>.  The average speed of the two-ways trip is 25.2 km.h
</pre>

Solved.