SOLUTION: The excursion boat on the river takes 2� hours to make the trip to a point 12 miles upstream and to return. If the rate at which the boat travels in still water is 5 times the rate

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Question 1015971: The excursion boat on the river takes 2� hours to make the trip to a point 12 miles upstream and to return. If the rate at which the boat travels in still water is 5 times the rate of the river current, what is the rate of the current?
Which of the following equations can be used to solve for c, the rate of the current?

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
The excursion boat on the river takes 2� hours to make the trip to a point 12 miles upstream and to return.
If the rate at which the boat travels in still water is 5 times the rate of the river current, what is the rate of the current?
:
let c = rate of the current
then
5c = rate of the boat in still water
therefore
5c - c = 4c is the effective speed upstream
and
5c + c = 6c is the effective speed downstream
:
Write a time equation; time = dist/rate
up time + down time = 2.5 hrs
+ = 2.5 is the equation we use to solve this
:
multiply equation by 12c
12c* + 12c = 12c(2.5)
cancel the denominators and you have
3(12) + 2(12) = 30c
36 + 24 = 30c
60 = 30c
c - 60/30
c = 2 mph is the rate of of the current