SOLUTION: Al travels in his motorboat downstream 12 miles with the current. He then turns around and heads back to the starting point going upstream against the current. The total time of hi

Question 1119371: Al travels in his motorboat downstream 12 miles with the current. He then turns around and heads back to the starting point going upstream against the current. The total time of his trip is 5 hours and the river current is 2 miles per hour. If during the entire trip he did not change speed, find the speed of the boat in still water
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.

Let "u" be the boat speed in still water, in miles per hour.


Then the boat' speed downstream is (u+2) miles per hour, while

     the boat' speed downstream is (u-2) miles per hour.


Time to travel downstream is  hours, while

time to travel upstream is   hours.


The total time is   +   hours.


According to the condition, it is 5 hours, which gives you an equation

     +  = 5.


To solve it, multiply both sides by (u+2)*(u-2) = (u^2-4).  You will get


    12*(u-2) + 12*(u+2) = 5*(u^2-4)


    12u - 24 + 12u + 24 = 5u^2 - 20,

    5u^2 - 24u - 20 = 0


     =  = .


Only positive root works  u =  = 5.524.


Answer.  The boat' speed in still water is 5.524 miles per hour.


Check.    = 5.00 hours.   ! Correct !

Solved.

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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
    - Wind and Current problems
    - More problems on upstream and downstream round trips
    - Wind and Current problems solvable by quadratic equations
    - Unpowered raft floating downstream along a river
    - Selected problems from the archive on the boat floating Upstream and Downstream
in this site, where you will find other similar solved problems with detailed explanations.

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
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

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

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

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