To paint a house, two painters are hired. the first painter can paint the entire house in ten hours. the second painter will need six hours to paint the entire house. if the two painters start painting at 8: 00 am, at what time will they finish painting the house?

Let's think what will happen at 10: (after two hours)
the first painter will have pained two tenths of the house - that is 20%.
the second painter will have painted two sixths of the house- that is 33%
Together they will have pained 20%+33%, that is 53%.
 
Let's think what will happen at 11: (one hour later)
the first painter will have pained one tenth of the house - that is 10%.
the second painter will have painted one sixth of the house- that is 16.5%
Together they will have pained 10%+16.5%, that is 26.5%. Together with the previous portion we have 53%+26.5%=79.5%

Half an hour later (at 11:30) they will have painted half of 26.5%, that is 13.25, so together it's 92.75%,
But at 12 they will have painted 92.75+13.25=106%, which is more than a full house!

So the correct answer is: between 11:30 and 12! (around 11:45 actually)
Another solution:
(the first painter paints 1/10 in an hour and the second 1/6 in a hour, so together they paint 1/10+1/6 every hour, which is 3/30+5/30=8/30=4/15th of the house. there are 4 quarters every hour, so they paint 1/15 every quarter)

after 3 hours they will have painted 3*4/15=12/15 of the house and they still have 3/15 - they need 45 mins to do this!)