This was a problem I did with my
students in Calculus 151c (that's
differential calculus at
OSU). The students seemed to like it... It's a fairly
basic rate problem, I think it's a really good
problem because it ties together the relationship between
rates,
derivatives, and
integrals. Here goes...
The Beer Bong Problem
Jim is a
college student, and like many others, he likes to spend his weekend
drinking at parties. At the party in question, Jim is invited to drink from a
beer bong, and he accepts. Before he begins, the bong is filled with 12 ounces of
beer. Jim can drink beer at an initial rate of 1.5 ounces per second. However, as he drinks and runs out of
breath, the rate at which he can drink decreases by a constant
factor. Of course, Jim's friends will be adding more beer to the
bong at a rate of 2 ounces per second. Assume the bong can hold a maximum of 22
ounces of beer.
a) Give an equation for the amount of beer in the bong at any time t
b) Assuming the constant factor of decreasing drinking rate is .1 ounces per second, will the bong overflow before Jim is finished drinking?
c) Find a constat that that will leave the bong empty just as Jim is finished drinking (to minimize waste of beer)
Note: I'll post the solution to this tomorrow, time for bed now :)