SOLUTION
We are told that the barrel can contain 60 gallons of water.
This barrel has a hole at its bottom and leaks out 2 gallons every hour, that is it loses 2 gallons every 1 hour.
This means that it will lose 4 gallons after 2 hours.
Since it loses 2 gallons every hour, that means it would lose 1 gallon every half hour or every 30 minutes.
Therefore after 2 and half hours, it would lose
4 gallons after 2 hours and 1 gallon after half hour, making a total of 5 gallons.
Therefore the answer is 5 gallons