Question 1130467: Karen paddled A canoe 10 miles upstream and then paddled back to the starting point. If the rate of the current was 3 MPH and the entire trip took 3.5 hours, what was her rate?
Answer by ikleyn(52786)   (Show Source):
You can put this solution on YOUR website! .
If x is the rate of the canoe in still water, then
(x+3) mph is the effective speed downstream, and
(x-3) mph is the effective speed upstream.
So,  is the time downstream, while  is the time upstream, so the "time" equation is
+ = 3.5 hours. (*)
At this point the setup is completed.
To complete the solution, reduce equation (*) to a quadratic equation by multiplying its both sides by 2*(x+3)*(x-3) and solve.
The rest is just arithmetic.
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To see many similar solved problems, look into the 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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