<p>Is there an equation for the questions asking along the lines
"If Tom paints in 2 hours and Jill paints in 5 hours, How long will it take if they work together?"</p>
<p>If the area to be painted is x square feet, then Tom paints at a rate of (x/2) sq.feet/hour and Jill at a rate of (x/5) sq.feet/hour. Together, in a single hour they will paint
(x/2) + (x/5) = (5x/10) + (2x/10) = 0.7x sq.feet/hour</p>
<p>So, time to paint the area if they work together = (total square feet) / (sq.feet painted per hour)
= x / (0.7x) = 10/7 or 1.43 hours</p>
<p>I don't even think they do this anymore, but anyway, I find the best way to do this is find out how much of the house they each paint in one hour. So Tom paints 1/2 the house in one hour and Jill paint 1/5 of the house in an hour. So together they paint 7/10 of the house in one hour, thus you can solve from here:</p>
<p>[7/10]x = 1</p>
<p>x = 10/7 = 1.4285 hours = 1 hr. 25 minutes 42 seconds and little bit :D</p>