'A mason can build a wall in one-half the time it takes an apprentice. Together they build the wall in 12 hours. How long would it take the apprentice working alone to build the wall?' This needs to be worked using a table. The column headings are 'Time Alone', 'Rate', 'Time Together' and 'Work Accomplished'.

If this is algebra, you should not have to make tables.

Let the mason's rate be x walls per hour and the apprentice's rate be 0.5 x walls per hour. Working together, their rate is 1.5x walls per hour.

1.5x * 12 h = 1 wall
x = 1/18 wall per hour
x/2 = 1/36 wall per hour
The apprentice alone would need 36 hours

To solve this problem using a table, we can break it down into steps. Let's fill in each column of the table one by one.

Column headings:
1. Time Alone: The time it takes for each worker to build the wall alone.
2. Rate: The rate at which each worker completes the work.
3. Time Together: The time it takes for both workers to build the wall together.
4. Work Accomplished: The portion of the work completed by each worker.

Now let's fill in the table step by step:

Step 1: Let's assume the apprentice's time alone is "x" hours. So the mason's time alone will be "x/2" hours.

Step 2: The rate can be calculated by dividing the work accomplished by the time taken. Since the work accomplished is the same for both workers, we can say that the rate for the apprentice is 1/x and for the mason is 1/(x/2).

Step 3: The time taken when both workers work together is given as 12 hours.

Step 4: The work accomplished by each worker can be calculated using the formula: Work Accomplished = Rate * Time.

Now let's fill in the table:

| Time Alone | Rate | Time Together | Work Accomplished |
|--------------|------------|---------------|-------------------|
| x | 1/x | 12 | 1/12 |
| x/2 | 2/x | 12 | 1/12 |

From the table, we can see that when the mason works alone, he does the work in x/2 hours, and the rate is 2/x. The work accomplished by both workers together is 1/12.

Since the mason can build the whole wall in x/2 hours, which is equal to 1/12 of the work, we can set up an equation:

1/12 = 2/x (because the mason works twice as fast as the apprentice, so the work accomplished by the mason is twice that of the apprentice)

By solving this equation, we can determine the value of x, which represents the time the apprentice takes to build the wall alone.

Multiplying both sides of the equation by 12x, we get:

x = 24

So, it would take the apprentice 24 hours to build the wall alone.