SOLUTION: A boat travels 27 miles downstream in 3 hours, and when traveling upstream it takes twice as much time to travel 2/3 of that distance. Find the rate of the boat in still water and

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Question 398162: A boat travels 27 miles downstream in 3 hours, and when traveling upstream it takes twice as much time to travel 2/3 of that distance. Find the rate of the boat in still water and the rate of the current.
Answer by ankor@dixie-net.com(22740) (Show Source):
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A boat travels 27 miles downstream in 3 hours, and when traveling upstream
it takes twice as much time to travel 2/3 of that distance.
Find the rate of the boat in still water and the rate of the current.
:
Find the upstream distance: *27 = 18 miles
:
Let s = boat speed in still water
Let c = current speed
then
(s-c) = effective speed upstream
and
(s+c) = effective speed downstream
:
Write a distance equation for each way
:
3(s+c) = 27
6(s-c) = 18
Simplify both equations, divide the 1st by 3, and the 2nd by 6, results:
s + c = 9
s - c = 3
------------addition eliminates c, find s
2s = 12
s = 6 mph is the boat speed in still water
and
6 + c = 9
c = 3 mph is the current speed
:
:
Check solutions by finding the distance
3(6+3) = 27
6(6-3) = 18