Question 829334
Let's start from here, the correct equation for their combined rate: {{{1/12+1/8=1/x}}}.


{{{2/24+3/24=1/x}}}... but instead of solving for x, just compute the rate.  That is what you really want, even if it is as a rational number, fraction form.


That is {{{highlight_green(5/24)}}} batches per hour.
You can also say, 5 batchs in 24 hours.


Next, look at time values, not necessarily viewed on a number line.  Time 8AM is time, ZERO.  Let h be the time after the first hour, because Mona joins Bart after ONE hour.  Bart works for 1+h hours and Mona works with him for h hours.


The total jobs done will be 1.
This one job is {{{jobByBart+jobByBoth=1}}};
{{{highlight_green(highlight((1/12)*1+(5/24)(h+1)=1))}}}
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Most important is to understand the analysis, and the resulting equation.  Solving it for h should be much less of a chore.