Question

. A 1000-gallon tank initially contains a mixture of 450 gallons of cola and 50 gallons of cherry syrup. Cola is added at the rate of 8 gallons per minute, and cherry syrup is added at the rate of 2 gallons per minute. At the same time, a well mixed solution of cherry cola is withdrawn at the rate of 5 gallons per minute. What percentage of the mixture is cherry syrup when the tank is full

Answer 1

The tank is filled up at a total rate of 10 gal/min, and currently contains 500 gal of solution. It can hold up to 1000 gal, so it will take time t to fill it up completely:

500 gal = (10 gal/min) t

t = (500 gal) / (10 gal/min)

t = 50 min

In that time,

(8 gal/min) (50 min) = 400 gal of cola

and

(2 gal/min) (50 min) = 100 gal of cherry syrup

are added to the tank, so that when it's full, the tank contains 850 gal of cola and 150 gal of syrup.

So 150 gal of the total 1000 gal of solution is cherry syrup, or (150 gal)/(1000 gal) = 15/100 = 15% of the mixture.