SOLUTION: Can anyone help me set this up and solve? I am having some trouble with this conceot. Thank you. Alvin paddled for 2 hours with a 6-km/h current to reach a campsite. The retur

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Can anyone help me set this up and solve? I am having some trouble with this conceot. Thank you. Alvin paddled for 2 hours with a 6-km/h current to reach a campsite. The retur      Log On


   

Question 1125847: Can anyone help me set this up and solve? I am having some trouble with this conceot. Thank you.
Alvin paddled for 2 hours with a 6-km/h current to reach a campsite. The return trip against the same current took 8 hours. Find the speed of the boat in still water.
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let u be he speed of the boat in still water.


Then the effective speed downstream is u+6 km/h.

So the distance downstream is  2*(u+6) kilometers.


The effective speed upstream is  (u-6) km/h.

So the distance upstream is     8*(u-6) kilometers.


Each way distance is the same, which gives you an equation


    2*(u+6) = 8*(u-6).


Simplify and solve it:


    2u + 12 = 8u - 48,

    12 + 48 = 8u - 2u

    60  = 6u    ====>  u = 60/6 = 10 kilometer per hour.


Answer.  The speed of the boat in still water is  10 km/h.

Solved.

Make a check on your own - and you will understand the solution even better.

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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.