This is a work problem. We can use theories on ratios and proportion in order to solve this. We do as follows:
Faucet A = 8 minutes to fill
Faucet B = 12 minutes to fill
1/8 + 1/12 = 1/x
let x represent the time it takes for both to fill the cooler
x = 4.8 minutes for both to fill the cooler