Question 1185907
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A boat travels 20 km/h in still water. If this boat goes upstream in a river flowing at a rate of 6 km/h for 10 km, 
and then 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 speed upstream   is   u = 20-6 = 14 km/h


The speed downstream is   v = 20+6 = 26 km/h.


The average speed of the whole roundtrip is  {{{(2uv)/(u+v)}}} = {{{(2*14*26)/(14+26)}}} = 18.2 km/h.    <U>ANSWER</U>
</pre>

Solved.



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The key of my solution is to use the formula  &nbsp;&nbsp;{{{(2uv)/(u+v)}}}  &nbsp;&nbsp;for the average speed of the whole roundtrip.



Also notice, &nbsp;that this formula and the answer &nbsp;DO &nbsp;NOT &nbsp;DEPEND &nbsp;on the length of the trip: &nbsp;&nbsp;for example, 

if the length is &nbsp;40 &nbsp;kilometers in each of the two directions (instead of 10 kilometers in your problem), 

the answer for the average speed of the roundtrip will be the same.



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For your education, &nbsp;see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A /HREF=http://www.algebra.com/algebra/homework/word/travel/Calculating-an-average-speed.lesson>Calculating an average speed: a train going from A to B and back</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/One-more-problem-on-calculating-an-average-speed.lesson>One more problem on calculating an average speed</A>  

in this site.