A painter can paint a fence in 12 hours working alone. His apprentice who works slower can paint the same fence in 24 hours. How many hours would it take to do the job if they worked together?

how much of the total job gets one in 1 hour if they work together?

1/12 + 1/24 = 1/8

so, together they can do the job in 8 hours.

To find out how many hours it would take for the painter and his apprentice to paint the fence together, we can use the concept of work rates.

First, let's determine the work rate, or the amount of work each person can complete per hour. We can calculate this by dividing the amount of work (which is painting the entire fence) by the time taken to complete the work.

The painter can paint the fence in 12 hours, so his work rate is 1/12 of the fence per hour.
The apprentice can paint the fence in 24 hours, so his work rate is 1/24 of the fence per hour.

To find out how much work they can complete together in one hour, we can add their work rates:

1/12 + 1/24 = 1/8

The combined work rate of the painter and the apprentice is 1/8 of the fence per hour.

Since we know their combined work rate, we can determine how long it would take them to paint the entire fence together. To do this, we divide the amount of work (which is painting the entire fence) by their combined work rate:

1 / (1/8) = 8

Therefore, it would take the painter and his apprentice 8 hours to complete the job if they worked together.