Ahomeowner estimates that it will take him 13 days to roof his house. a professional roofer estimates that he could roof the house in 4 days. how long will it take if the homeowner the roofer?

Approximately 3 days

Step-by-step explanation:

A homeowner estimates that it will take him 13 days to roof his house.

The homeowner's unit rate of working (per day) would be 1/13

A professional roofer estimates that he could roof the house in 4 days.

The professional roofer's unit rate of working (per day) would be 1/4

Since the homeowner is helping the professional roofer, their unit rates would be combined. This combined rate is additive since they would be working simultaneously or at the same time.

Assuming if they work together, it will take t days, this means that their combined rate is 1/t. Therefore,

1/13 + 1/4 = 1/t

(4+13)/52= 17/52 = 1/t

17t = 52

t = 52/17 = 3.06

It will take both of them approximately 3 days to roof the house