The percentage of alcohol initilly is .
The vat contains the beer is .
Initially the alcohol in the vat is .
The percentage of alcohol pumped into the vat at a rate of .
The percentage of alcohol pumped out the vat at a rate of .
Let be the amount of alcohol after time .
Rate of change in percentage alcocohol is the percentage of alcohol pumped into vat minus percentage of alcohol pumped out of the vat.
Rate of change in alcohol is .
Rate of alcohol pumped into the vat is .
Rate of alcohol pumped out the vat is .
Substitute corresponding vakues in the above equation.
Apply integration on each side.
Solve for constant .
.
Substitute and in the above equation.
Find the percentage of alcohol after an hour.
The percentage of alcohol after time is .
Here time .
Substitute and in .
Substitute and in .
.
The percentage of alcohol after an hour is .
The percentage of alcohol after an hour is .
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