Question 1137361: A kayak can travel 30 miles downstream in 5 hours, while it would take 15 hours to make the same trip upstream. Find the speed of the kayak in still water, as well as the speed of the current. Let k represent the speed of the kayak in still water, and let c represent the speed of the current.
Answer by ikleyn(52819)   (Show Source):
You can put this solution on YOUR website! .
The speed of the kayak downstream,  = 6 miles per hour, is the sum k + c.
The speed of the kayak upstream,  = 2 miles per hour, is the difference k - c.
So, you have these two equations
k + c = 6, (1) and
k - c = 2 (2)
Add the equation to eliminate "c" and to get
2k = 6 + 2 = 8, k = 8/2 = 4 miles per hour.
Then from equation (1), c = 6 - k = 6 - 4 = 2.
Answer. Kayak speed in still water is 4 mph. The speed of the current is 2 mph.
CHECK. Check the solution on your own, by substituting the found values into the condition.
Solved, explained and completed.
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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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