This was a problem I did with my students
in Calculus 151c (that's differential calculus
). 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 rate
s, 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 ounce
s 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 :)