If it takes painter # 1 three hours to paint a house, and painter # 2 eight hours to paint a house, how long would it take them if they work together?

#1's rate = house/3

#2's rate = house/8
combined rate = house/3 + house/8
= 11house/24

so time for combined effort = house/(11house/24)
= 24/11 hours

To figure out how long it would take the two painters to paint the house if they work together, we need to calculate their combined work rate.

Painter #1 takes 3 hours to paint a house, which means his work rate is 1/3 of a house per hour (1 house / 3 hours = 1/3).

Painter #2 takes 8 hours to paint a house, so his work rate is 1/8 of a house per hour (1 house / 8 hours = 1/8).

To get their combined work rate, we add their individual work rates together:

1/3 + 1/8 = 8/24 + 3/24 = 11/24

Therefore, when the two painters work together, their combined work rate is 11/24 of a house per hour.

Now, to find out how long it would take for them to paint the house together, we can take the reciprocal of their combined work rate:

1 / (11/24) = 24/11

So, it would take them approximately 2.18 hours (24/11 hours) to paint the house if they work together.