SOLUTION: In still water, a boat averages 18 miles per hour. In a river, it takes the same amount of time to travel 33 miles downstream as it takes to travel 21 miles upstream. What is the r

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Question 848814: In still water, a boat averages 18 miles per hour. In a river, it takes the same amount of time to travel 33 miles downstream as it takes to travel 21 miles upstream. What is the rate of the rivers current?
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
c = speed of the river current
t = the same amount of time for the up and down streams distances
18 = boat speed when not in any current

Model uniform rate equation for travel is R*T=D, Rate, Time, Distance.

__________________speed__________time___________distances
downstream________18+c___________t______________33
upstream__________18-c___________t______________21

The downstream equation is %2818%2Bc%29t=33;
18t%2Bct=33
-
the upstream equation is %2818-c%29t=21;
18t-ct=21.
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Two nonlinear equations in two unknowns c and t. The situation in the example allows for the elimination method for the term highlight_green%28ct%29. Add the left members and equate to the addition of the right-side members.

18t%2Bct%2B18t-ct=33%2B21
36t%2B0=54
t=54%2F36

highlight%28t=%283%2F2%29%29

The question is for the speed of the current, c.
Solve either travel equation for c and then use the now found t to compute c.
-
18t-ct=21
-ct=21-18t
c=%2821-18t%29%2F%28-t%29
highlight%28highlight%28c=%2818t-21%29%2Ft%29%29