SOLUTION: Jake paddled a canoe 4 miles upstream at a constant speed of 10 mph. He then turned around and paddled downstream until he reached his original starting place. If the entire trip t

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Question 927673: Jake paddled a canoe 4 miles upstream at a constant speed of 10 mph. He then turned around and paddled downstream until he reached his original starting place. If the entire trip took him 9 hours, how fast was the speed of the river current?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Jake paddled a canoe 4 miles upstream at a constant speed of 10 mph.
He then turned around and paddled downstream until he reached his original starting place.
If the entire trip took him 9 hours, how fast was the speed of the river current?
:
let c = speed of the current
Assuming that 10 mph was his paddling speed in still water, then:
(10-c) = his effective speed upstream
and
(10+c) = his effective speed down stream
:
Write a time equation; time = dist/speed
time up + time down = 9 hrs
4%2F%28%2810-c%29%29 + 4%2F%28%28s%2Bc%29%29 = 9
multiply equation by (10-c)(10+c), cancel the denominators
4(10+c) + 4(10-c) = 9(10-c)(10+c)
40 + 4c + 40 - 4c = 9(100 - c^2)
80 = 900 - 9c^2
9c^2 = 900 - 80
9c^2 = 820
c^2 = 820/9
c^2 = 91.1
c = sqrt%2891.1%29
c = 9.545 mph is the rate of the current
:
:
Pretty hefty current, see if this checks out
4/19.545 ~ .2 hrs down stream
4/.455 ~ 8.8 hrs up stream
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total time 9 hrs