SOLUTION: A boat takes 4 hours to travel 36 miles downstream and 12 hours for the return trip. What is the speed of the current and the speed of the boat in still water?

Question 530140: A boat takes 4 hours to travel 36 miles downstream and 12 hours for the return trip. What is the speed of the current and the speed of the boat in still water?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The apparent speed is 9mph with the current and 3 mph against the current.
The average is the speed of the boat in still water (6mph) and the difference is the speed of the current (3mph).
However, the intention of the problem must have been to set and solve a system of equations, so let's get silly.
Let be the speed of the boat in still water in mph, and
be the speed of the current in mph.
We could say that the total speed going downstream, in mph, is

and that the total speed for the return trip, in mph, is

Then we solve the system of equations.
We could do it by substitution, solving for
in the second equation
and substituting that into the first equation to get
so , so so
Then we substitute that solution in
and find so
We could also solve by other methods, but it's Friday night and I have other stuff to do.
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