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.
