Question 816246
The trick with these problems is that you are told how long someone would take to do the whole task. In this case 8 days for one painter and 5 days for the other. But what you want/need is: How much of the task can someone do in one unit of time?<br>
In this case you want to know how much (what fraction) of the job can be completed by each painter within one day? If it takes one painter 8 days to complete the job then he/she could do 1/8 of the job in one day. And the other painter can so 1/5 of the job in 1 day.<br>
The combined rate of the two painters would be:
{{{1/8+1/5}}}
To add these we need a common denominator:
{{{5/40+8/40}}}
{{{13/40}}}
So together the painters can paint 13/40 of a house in one day. To find out how long it would take to complete the job, use the reciprocal:
{{{40/13}}}
or
{{{3&1/13}}} days