Question 1089552
.
Julie and Eric row their boat (at a constant speed) 63 miles downstream for 7 hours, helped by the current. 
Rowing at the same rate, the trip back against the current takes 9 hours. Find the rate of the current.
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<pre>
Let u be the rate of the boat in a still water (at no current), in miles per hour.
Let v be the rate of the stream.


Then the rate rowing downstream is (u+v) relative to the river banks.

From the other side, this rate is {{{63/7}}} = 9 mph, according to the condition, 

It gives you your first equation

u + v = 9.    


The rate rowing upstream is (u-v) relative to the river banks.

From the other side, this rate is {{{63/9}}} = 7 mph, according to the condition, 

It gives you your second equation

u - v = 9.    


Combining equations (1) and (2) together, you get the system of two equations

u + v = 9,     (1)
u - v = 7.     (2)


To solve the system, add the equations (1) and (2). You will get

2u = 9 + 7 = 16  ====>  u = {{{16/2}}} = 8.


Thus you found that the rate of the boat in the still water is 8 miles per hour.

Then from (1), v = 9 - u = 9 - 8 = 1 mph.


<U>Answer</U>.  The rate of the current is 1 mile per hour.
</pre>

Solved.



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=http://www.algebra.com/algebra/homework/word/travel/Wind-and-Current-problems-solvable-by-quadratic-equations.lesson>Wind and Current problems solvable by quadratic equations</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Unpowered-raft-moving-downstream-along-a-river.lesson>Unpowered raft floating downstream along a river</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, &nbsp;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>", &nbsp;the topic "<U>Travel and Distance problems</U>".