Tom can paint the fence in 12 hours, but if he works together with a friend they can finish the job in 8 hours. How long would it take for his friend to paint this fence alone?

It takes his friend 24 hours

Step-by-step explanation:

The formula for time on a job is

1/A + 1/B = 1/C

where A is the time for person A

B is the time for person B

C is the time for A and B together

Tom is person A and his friend is person B

1/12 + 1/B = 1/8

The Common denominator is 24, so multiply by 24 on each side

24 (1/12 + 1/B) = 1/8*24

2 + 24/B = 3

Subtract 2 from each side

2-2 + 24/B = 3-2

24/B = 1

Multiply each side by B

24/B * B = B*1

24 = B