Question 805262
Look at rates according to jobs per time.  "Paint the house" is the one job and time is in number of days.


Given an amount of days, d, agent A works at the rate of 1/d jobs per day and agent B works at the slower rate of 1/(2d) jobs per day.


When agents A and B work at the same time, the needed time for 1 job is 6 days.


{{{highlight(r*t=j)}}}
r = rate
t = time in days
j = how many jobs.


This rate for A and B together is {{{1/(2d)+1/d}}}.
We are given the time for their one job, {{{t=6}}}.
We understand that {{{j=1}}} for 1 job.


The rate is what is unknown because the rate contains variable d, which is what we must solve for.
{{{highlight(highlight((1/(2d)+1/d)*6=1))}}}


Solving for d should be uncomplicated.  The rate for each of A and B can be computed using d.