Okay, well, since the
rate of
consumption is 1.5-kt, the total consumption (assuming 0 initial consumption) is 1.5t-kt
2/2, and it gets
filled at a rate of 2t, so the answer to
a) is b(t)=12+.5t-kt
2/2.
The answers for b) and c), however, rely on common sense - if his drinking rate starts at 1.5oz/sec and only decreases, then his drinking rate will NEVER overtake the filling rate of 2.0oz/sec. So the bong will certainly overflow no matter what - unless you have a negative constant (which defies the setup of the problem).
Also, how is "done drinking" defined, anyway? The time at which the bong is empty? Then the answer to c) is circular anyway. Or perhaps it's the time at which Jim's ability to drink has been expended (i.e. 1.5-kt=0)? Who knows?
In any case, this problem has many, many holes in it. I'd like to see your solution, ccunning, if you don't mind... :)