A homeowner estimates that it will take 9 days to roof his house. A professional roofer estimates that he could roof the house in 5 days. How long ( in days ) will it take if the homeowner helps the roofer?

Respuesta :

Solution:

If x denote the days, the rate unit being Jobs per day is:

[tex]\frac{1}{x}=\frac{1}{9}+\frac{1}{5}[/tex]

this is equivalent to

[tex]\frac{1}{x}=\frac{5+9}{45}=\frac{14}{45}[/tex]

solving for x, we get:

[tex]x\text{ = }\frac{45}{14}=3.2\text{ days}[/tex]

that is just a little more than 3 days.