Question

A vat with 200 gallons of beer contains 4% alcohol (by volume). Beer with 6% alcohol is pumped into the vat at a rate of 2 gal/min and the mixture is pumped out at the same rate. What is the percentage of alcohol after an hour? (Round the answer to one decimal place.)

Answer 1

Answer:

The percentage of alcohol after an hour is 4.8% (rounded to one decimal place)

Step-by-step explanation:

The vat initially has 200 gallons of beer with 4% alcohol by volume. 2gal/min of alcohol is added (containing 6% alcohol) for an hour.

STEP 1: FINDING THE TOTAL VOLUME OF BEER IN THE VAT

The volume of beer containing (containing 6% alcohol) after an hour = 2 * 60 = 120 gallons of beer.

The total volume of beer in the vat after an hour = 200 gal + 120 gal = 320 gal

STEP 2: FINDING THE TOTAL VOLUME OF ALCOHOL IN THE BEER AFTER AN HOUR

The volume of alcohol in the initial beer = 4/100*200 = 8 gal

The volume of alcohol in the beer being added at a constant rate = 6/100*120 = 7.2 gal

The total volume of alcohol in the vat after an hour = 8 gal + 7.2 gal = 15.2 gal

STEP 3: FINDING THE PERCENTAGE OF ALCOHOL AFTER AN HOUR

%of alcohol after an hour = total volume of alcohol in the beer after an hour /total volume of beer in the vat after an hour *100%

%of alcohol after an hour = 15.2/320*100% = 0.0475 * 100%

=4.75% = 4.8% (rounded to one decimal place)