In preparation for the holiday season, M&M is packaging red and green M&Ms toget
ID: 2902556 • Letter: I
Question
In preparation for the holiday season, M&M is packaging red and green M&Ms together. The packing machine consists of a very large mixing vat containing 500 gallons of red M&Ms and 500 gallons of green M&Ms. There are two streams, one red the other green, of M&Ms flowing into the tank, each at a rate of 10 gallons per minute. The well mixed M&Ms flow out of the vat into packages at a rate of 20 gallons per minute. A colorblind employee accidentally pours an additional 100 gallons of blue M&Ms into the vat.
(a) Set up an initial value problem that models the situation after the accident.
(b) Find an expression for the amount of blue M&Ms in the vat at time t.
(c) How much time must pass before the percentage of blue M&Ms in the tank drops below 1%?
Explanation / Answer
a) Q' = -(20/1100)Q
b) Q(t) = 100e^-(t/55)
c) t = 55ln(100/11)