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:

And the downstream trip is described by:

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 , so:

Multiply both sides by to get rid of the denominator:

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