Given:
John takes 8 hours to do 4 people's hair.
a.) The unit rate.
[tex]\text{ Unit Rate = Constant of Proportionality }\rightarrow\text{ k = }\frac{y}{x}[/tex]Let,
x = No. of hours ; The no. of hours the hairstylist took/invested.
y = No. of people ; This is the output of the hairstylist.
We get,
[tex]\text{ k = }\frac{y}{x}\text{ }\rightarrow\text{ k = }\frac{4}{8}\text{ = }\frac{1}{2}[/tex]Therefore, the equation in getting the no. of haircuts will be,
[tex]\text{ y = }\frac{1}{2}x\text{ ; with unit rate of 1/2}[/tex]b.) How many haircuts could John do in 2 hours. Let, x = 2.
[tex]\text{ y = }\frac{1}{2}(2)\text{ }\rightarrow\text{ y = }\frac{2}{2}\text{ }\rightarrow\text{ y = 1}[/tex]Therefore, John could do 1 haircut in 2 hours.
c.) How many haircuts will there be in 5 hours? Let, x = 5.
[tex]\text{ y = }\frac{1}{2}(5)\text{ }\rightarrow\text{ y = }\frac{5}{2}\text{ }\rightarrow\text{ y = 2 }\frac{1}{2}\text{ or 2.5}[/tex]Therefore, there will be 2 1/2 haircuts in 5 hours.