Let's calculate the ratio of vinegar to water when the contents of both glasses are mixed together.
In the first glass, the ratio of vinegar to water is 1:3. This means that for every 1 part vinegar, there are 3 parts water.
In the second glass, the ratio of vinegar to water is 1:4. This means that for every 1 part vinegar, there are 4 parts water.
To find the overall ratio when the contents are mixed, we need to consider the total amount of vinegar and water in both glasses.
Let's assume that the first glass has 1 unit of vinegar and 3 units of water. Therefore, the total amount of liquid in the first glass is 1 + 3 = 4 units.
The second glass has twice the capacity of the first glass, so it has 2 * 4 = 8 units of liquid.
When we mix the contents of both glasses together, we have a total of 4 + 8 = 12 units of liquid.
Now, let's calculate the total amount of vinegar and water in the mixture.
In the first glass, the ratio of vinegar to water is 1:3. So, in 4 units of liquid, we have 1 unit of vinegar and 3 units of water.
In the second glass, the ratio of vinegar to water is 1:4. So, in 8 units of liquid, we have 2 units of vinegar and 6 units of water.
When we combine the contents of both glasses, we have a total of 1 + 2 = 3 units of vinegar and 3 + 6 = 9 units of water.
Therefore, the ratio of vinegar to water in the mixture is 3:9, which can be simplified to 1:3.
So, the ratio of vinegar to water in the mixture is 1:3.