SOLUTION: If the owner of a house can paint it entirely in 20 days but a professional can paint in 14 days, then how much time will it take to paint the entire house if both painters worked

Question 1102774: If the owner of a house can paint it entirely in 20 days but a professional can paint in 14 days, then how much time will it take to paint the entire house if both painters worked together?
Please provide me steps. I don't know if I answered this correctly.
Found 2 solutions by Boreal, josgarithmetic:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
in one day, the owner paints 1/20 of the house
in one day, the professional paints 1/14 of the house
in x days, working together, they paint the whole house.
So, (x/20)+(x/14)=1
multiply by 140
7x+10x=140
17x=140
x=8.24 days ANSWER
8.24/20+ 8.24/14=1
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
R, rate
T, time
J, job, amount of work, piece of work
RT=J, basic work rates rule

The work rates for the owner and the professional painter can take the rate unit of , and if they work together, the individual rates are simply ADDED.

You really do not need to use the RT=J work rate rule.

Owner works at house per days.
Professional works at house per days.

Combined,

, in ;
You want the reciprocal for how many DAYS for 1 house.

About 8 and a quarter days.
RELATED QUESTIONS
Jean paints a house in 4 days. Brett can paint the same house in 6 days and Joe can paint (answered by rwm)
if a homeowner can paint a house in 14 days and a professional painter can paint it in 10 (answered by richwmiller,drk)
if a homeowner can paint a house in 14 days and a professional painter can paint it in 10 (answered by richwmiller)
Tyrin can paint a house in 4 days. Tahjai can paint the same house in 5 days. How many... (answered by bonster)
42. Tyrin can paint a house in 4 days. Tahjai can paint the same house in 5 days. How... (answered by vertciel)
what fraction of the house can Tim paint in d days? if he can paint a house in 6 days (answered by solver91311)
If one painter can paint a house in 5 days and another painter can paint the same house... (answered by ewatrrr)
A can paint a certain house in 10 days and B can paint the same house in 12 days. How... (answered by Alan3354)
Jose can paint a house in 10 days and peter can paint the same house in 12 days . how... (answered by nerdybill)