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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
(s-c) = effective speed upstream
(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
6 + c = 9
c = 3 mph is the current speed
Check solutions by finding the distance
3(6+3) = 27
6(6-3) = 18