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

Algebra ->  Customizable Word Problem Solvers  -> Travel -> 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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) About Me  (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