You have a 12 gallon bucket filled with water, and empty 7 and 5 gallon buckets. Without using any other measuring devices, and without estimating a half-way point on the buckets, how can you equally divide 6 gallons of water into 2 of the buckets.
PLEASE SHOW WORK
To equally divide 6 gallons of water into two buckets, one with a capacity of 7 gallons and the other with a capacity of 5 gallons, follow these steps:
1. Fill the 5-gallon bucket completely with water from the 12-gallon bucket.
- Now, you have 5 gallons of water in the 5-gallon bucket and 12-5 = 7 gallons of water remaining in the 12-gallon bucket.
2. Pour the water from the 5-gallon bucket into the 7-gallon bucket.
- The 7-gallon bucket was already partially filled by the initial step, so it can hold 7 - 5 = 2 gallons more.
3. Fill the 5-gallon bucket again with water from the 12-gallon bucket.
- Now, the 5-gallon bucket has 5 gallons of water, and the 7-gallon bucket has 2 + 5 = 7 gallons of water.
4. Pour the water from the 5-gallon bucket into the 7-gallon bucket until it is completely filled.
- The 7-gallon bucket needed 7 - 5 = 2 gallons more, and the remaining amount in the 5-gallon bucket is 5 - 2 = 3 gallons.
5. The 5-gallon bucket now has 3 gallons of water, and the 7-gallon bucket has 7 gallons of water.
In this way, you have equally divided 6 gallons of water using only the 12-gallon, 7-gallon, and 5-gallon buckets.