Question 1102774
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 {{{HOUSE/DAY}}}, 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  {{{1/20}}} house per days.
Professional works at  {{{1/14}}} house per days.


Combined,  {{{1/20+1/14=(1/20)(7/7)+(1/14)(10/10)}}}

{{{7/140+10/140}}}

{{{17/140}}}, in {{{HOUSES/DAY}}}; 

You want the reciprocal for how many DAYS for 1 house.


{{{140/17}}} {{{DAYS/HOUSE}}}

{{{highlight(8&4/17)}}}{{{days}}}

About 8 and a quarter days.