Answer: it will take Doug's son 6 days if he works alone
Step-by-step explanation:
It takes dad three days to re-roof a house. If his son helps him the job can be done in two days. This means that the time that the job takes will reduce because they worked together.
Let x = the number of days it will take Doug's son if he works alone,
Doug's unit rate of working will be 1/3
Doug son's unit rate of working will be 1/x
Their unit rates are additive because they will work simultaneously. Each will work at his own unit rate.
Combined unit rates will be
1/3 + 1/x = (x + 3)/3x
Since it will take 2 days if they work together, their combined unit rate will be 1/2
(x + 3)/3x = 1/2
2(x + 3) = 3x
2x + 6 = 3x
3x - 2x = 6
x = 6 days
