SOLUTION: A kayaker travels downstream 15 miles and then travels back upstream to a point which is 1 mile short of where he originally departed from. The entire trip takes 3 hours. in still

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A kayaker travels downstream 15 miles and then travels back upstream to a point which is 1 mile short of where he originally departed from. The entire trip takes 3 hours. in still       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 900400: A kayaker travels downstream 15 miles and then travels back upstream to a point which is 1 mile short of where he originally departed from. The entire trip takes 3 hours. in still water the kayaker paddles at a rate of 10 miles per hour. how fast is the current of the stream?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A kayaker travels downstream 15 miles and then travels back upstream to a point which is 1 mile short of where he originally departed from. The entire trip takes 3 hours. in still water the kayaker paddles at a rate of 10 miles per hour. how fast is the current of the stream?
------
Downstream DATA:
distance = 15 miles ; rate = 10+c mph ; time = d/r = 15/(10+c) hrs
----------------------------
Upstream DATA:
distance = 14 miles ; rate = 10-c mph ; time = d/r = 14/(10-c) hrs
---------------------------------------------------
Equation:
time + time = 3 hrs.
15/(10+c) + 14/(10-c) = 3 hrs
-------
15*(10-c) + 14(10+c) = 3(100-c^2)
------------------
150-15c + 140+14c = 300 - 3c^2
------
290 - c = 300 - 3c^2
----
3c^2 -c -10 = 0
3c^2 -6c + 5c -10 = 0
3c(c-2) + 5(c -2) = 0
(c-2)(3c+5) = 0
Positive solution:: c = 2 mph (speed of the current)
-------------------------------
Cheers,
Stan H.
------------------------