SOLUTION: Zene decides to canoe 6 miles upstream on a river to a waterfall and back. The total trip is 8 hours. She can canoe an average of 3 miles per hour. What is the speed of the current
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Question 194837: Zene decides to canoe 6 miles upstream on a river to a waterfall and back. The total trip is 8 hours. She can canoe an average of 3 miles per hour. What is the speed of the current? I would like more than just the answer, need to know how to get the answer. Thank you.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let r represent the rate of the current. Then 3 - r is the rate of the boat going upstream and 3 + r is the rate of the boat going downstream. Then let t be the time taken to go upstream which means that the time to go downstream must be 8 - t
Using 
, the upstream trip is then described by:
t)
And the downstream trip is described by:
(8 - t))
Solve each of these equations for t.
And
Now we have two expressions equal to t, so set them equal to each other:
Put everything on the left:
LCD is (3 - r) = 9 - r^2)
, so:
-6(3-r)-6(3+r)}{9-r^2} = 0)
Multiply both sides by 
to get rid of the denominator:
-6(3-r)-6(3+r) = 0)
Remove parentheses and collect like terms:
Only consider the positive root because we are reasonably certain that the current never went backwards during this trip, so:
Checking the answer is left as an exercise for the student.
John
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