Question

a vat with 600 gallons of beer contains 4% alcohol (by volume). beer with 6% alcohol is pumped into the vat at a rate of 6 gal/min and the mixture is pumped out at the same rate. what is the percentage of alcohol after an hour? (round your answer to one decimal place.)

Answer 1

The percentage of alcohol in the vat after one hour is 7.6%.

Step-by-step explanation:

To solve this problem, we need to consider the amount of alcohol added to the vat and the amount of beer that is pumped out. Let's break it down step by step:

1. Initially, the vat contains 600 gallons of beer with 4% alcohol. This means there are 600 gallons * 0.04 = 24 gallons of alcohol in the vat.
2. Every minute, 6 gallons of beer with 6% alcohol are pumped into the vat. This means 6 gallons * 0.06 = 0.36 gallons of alcohol are added each minute.
3. At the same rate, 6 gallons of the mixture are pumped out of the vat each minute.
4. After one hour, which is 60 minutes, there will be a total of 60 minutes * 0.36 gallons/minute = 21.6 gallons of alcohol added to the vat.
5. The total amount of alcohol in the vat will be 24 gallons (initial) + 21.6 gallons (added) = 45.6 gallons.
6. The total volume of the mixture in the vat after one hour will be 600 gallons (initial) + 60 gallons (added) - 60 gallons (pumped out) = 600 gallons.
7. To find the percentage of alcohol in the mixture, we can calculate: (45.6 gallons / 600 gallons) * 100% = 7.6% (rounded to one decimal place).