Question 1064441
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a motorboat can maintain a constant speed of 35 miles per hour relative to the water. the boat makes a trip upstream 
to a certain point in 30 minutes; the return trip takes 20 minutes. what is the speed of the current?
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<pre>
Let "v" be the speed of current, in miles per hour.

Then the motorboat speed with    the current is 35+v miles per hour.  ( the speed relative to the bank of the river )
     the motorboat speed against the current is 35-v miles per hour.  (-------------------- " --------------------- )

The distance for the trip downstream is the same as upstream:

{{{(1/2)*(35-v)}}} = {{{(1/3)*(35+v)}}}.   (1)

{{{1/2}}} is {{{1/2}}} of an hour = 30 minutes,

{{{1/3}}} is {{{1/3}}} of an hour = 20 minutes.

Multiply both sides of the eq.(1) by 6. You will get

3*(35-v) = 2*(35+v),

105 - 3v = 70 + 2v,

105 - 70 = 2v + 3v,

35 = 5v  ---->  v = {{{35/5}}} = 7 mph.

<U>Answer</U>. The current speed is 7 mph. The distance is {{{(1/2)*(35-7)}}} = 14 miles.

<U>Check</U>.  Time upstream {{{14/(35-7)}}} = {{{14/28}}} = {{{1/2}}} of an hour.

        Time downstream {{{14/(35+7)}}} = {{{14/42}}} = {{{1/3}}} of an hour.
</pre>


If you send me your comments/questions, please include the ID number of this problem (# 1064441) in order I could identify it.



It is a typical and standard Upstream and Downstream round trip word problem.

You can find many similar fully solved problems on upstream and downstream round trips with detailed solutions in lessons 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/Wind-and-Current-problems.lesson>Wind and Current problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/More-problems-on-upstream-and-downstream-round-trips.lesson>More problems on upstream and downstream round trips</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Selected-problems-from-the-archive-on-a-boat-floating-Upstream-and-Downstream.lesson>Selected problems from the archive on the boat floating Upstream and Downstream</A> 

in this site.


Read them attentively and learn how to solve this type of problems once and for all.


Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this textbook under the section "<U>Word problems</U>", the topic "<U>Travel and Distance problems</U>".