SOLUTION: If one painter can paint a house in 8 days and another painter can paint the same house in 5 days, how long will it take them to paint the house working together?

Question 816246: If one painter can paint a house in 8 days and another painter can paint the same house in 5 days, how long will it take them to paint the house working together?
Found 2 solutions by richwmiller, jsmallt9:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
1/8+1/5=1/x
5/40+8/40=1/x
12/40=1/x
3/10=1/x
x=10/3 days
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
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?

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.

The combined rate of the two painters would be:

To add these we need a common denominator:

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:

or
days
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