Hi Brandi,
Let's think about how long it would take to reroof the house if Doug's son also took 6 days to do it by himself.
We would guess that the two of them together would take half the time, or 3 days.
How do we get this mathematically?
Figure how much reroofing each one does in one day. . . each one does 1/6 of the roof in one day, so together they would finish 2/6 of the roof in one day. One whole roof divided by 2/6 (or 1/3) = 3 days.
Now for the real question. . . together Doug and his son will take 4 days. We already know that Doug finishes 1/6 of the roof in one day. To solve for how much of a roof his son finishes in one day, use the equation. . .
1/6 + X = 1/4 . . .together they finish 1/4 of a roof in one day
Subtract 1/6 from both sides . . .
X = 1/4 - 1/6
Common denominator . . . X = 3/12 - 2/12 = 1/12
So Doug's son finishes 1/12 of a roof in one day and he will need 12 days to finish the job by himself.
Dan
