I can’t remember how to answer this:
If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
1/4 + 1/6 = 1/x, so x = 12/5, or two hours and 24 minutes.
To add some English description:
If Sally can paint a house in 4 hours ( 1 house per 4 hours) then she can paint 1/4 house per hour. John can paint 1/6 house per hour. So how many hours (x) does it take for x*(1/4 + 1/6) = 1?
Another way of doing it:
The least common multiple of 4 hours and 6 hours is 12 hours.
Sally can paint 3 houses in 12 hours, and John can paint 2 houses in 12 hours.
So together they can paint 5 houses in 12 hours.
Therefore they can paint 1 house in 12/5 hours, or 2 hours and 24 minutes, as already shown by other methods.
Yet another way of looking at this is the formula for these work problems is exactly the same as the parallel resisitors formula. If you go to my calculator at:
http://www.1728.com/resistrs.htm
and enter 4 and 6 you will get an answer of 2.4 hours. (which equals 2 hours 24 minutes).
But if Sally is wearing her Daisy Mae’s and a baby doll t-shirt, John might not be as productive as if he worked alone.