SOLUTION: bill can row 3 mph in still water. it takes him 3 hours and 36 minds to go 3 miles upstream and return. find the speed of the current.

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Question 1110579: bill can row 3 mph in still water. it takes him 3 hours and 36 minds to go 3 miles upstream and return. find the speed of the current.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


3 hours 36 minutes is 3 3/5 hours, or 18/5 hours.

Let c be the rate of the current. Then Bill's speed upstream is 3-c, and his speed downstream is 3+c.

He is going 3 miles upstream and then 3 miles back; his total time is 3%2F%283-c%29%2B3%2F%283%2Bc%29. So
3%2F%283-c%29+%2B+3%2F%283%2Bc%29+=+18%2F5
3%283%2Bc%29%2B3%283-c%29+=+%2818%2F5%29%283-c%29%283%2Bc%29
9%2B3c%2B9-3c+=+%2818%2F5%29%289-c%5E2%29
18+=+%2818%2F5%29%289-c%5E2%29
5+=+9-c%5E2
c%5E2+=+4
c+=+2

Answer: the speed of the current is 2 mph.

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let r = speed of the current.


Then your "time" equation is


3%2F%283%2Br%29 + 3%2F%283-r%29 = 336%2F60


3%2F%283%2Br%29 + 3%2F%283-r%29 = 33%2F5


3%2F%283%2Br%29 + 3%2F%283-r%29 = 18%2F5


1%2F%283%2Br%29 + 1%2F%283-r%29 = 6%2F5


5*(3-r) + 5*(3 + r) = 6%2A%289-r%5E2%29


30 = 54 - 6r^2


5 = 9 - r^2


r^2 = 9-5 = 4  ====>  r = sqrt(4) = 2.


Answer.  Speed of the current is 2 km/h.

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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.

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.