Answer :
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!)
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!)
