In preparation for holiday season, M&M is packaging red and green M&Ms together. Packing machine comprises of the very large mixing vat having 500 gallons of red M&Ms and 500 gallons of green M&Ms. There are 2 streams, one red the other green, of M&Ms flowing into tank, each at the rate of 10 gallons per minute. Well mixed M&Ms flow out of vat into packages at the rate of 20 gallons per minute. The colorblind employee accidentally pours the extra 100 gallons of blue M&Ms into the vat.
i) Establish the initial value problem which models situation after accident.
ii) Determine the expression for amount of blue M&Ms in vat at time t.
iii) How much time should pass before percentage of blue M&Ms in tank drops below 1%?