SOLUTION: Rick paddled up the river, spent the night camping, and then paddled back. He spent 10 hours paddling and the campground was 24 miles away. If Rick kayaked at a speed of 5 mph, wha

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Rick paddled up the river, spent the night camping, and then paddled back. He spent 10 hours paddling and the campground was 24 miles away. If Rick kayaked at a speed of 5 mph, wha      Log On


   

Question 1117676: Rick paddled up the river, spent the night camping, and then paddled back. He spent 10 hours paddling and the campground was 24 miles away. If Rick kayaked at a speed of 5 mph, what was the speed of the current (in mph)?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
up           5-c     24/(5-c)    24
Down         5+c     24/(5+c)    24
total                 10

Equation to Solve: highlight_green%2824%2F%285-c%29%2B24%2F%285%2Bc%29=10%29

12%285%2Bc%29%2B12%285-c%29=5%2825-c%5E2%29

-
60%2B12c%2B60-12c=125-5c%5E2
120=125-5c%5E2
125-120=5c%5E2
5c%5E2=5
.
c%5E2=1
highlight%28c=1%29





...redone...

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
As soon as you got this equation (the "time" equation)

24%2F%285%2Bc%29 + 24%2F%285-c%29 = 10,


you can obtain (to guess) the correct solution MENTALLY and MOMENTARILY c = 1 mile per hour.


Check.  24%2F%285%2B1%29 + 24%2F%285-1%29 = 24%2F6 + 24%2F4 = 4 + 6 = 10 hours.

Any other answer is INCORRECT.

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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.