Answer:
b) 1.8 hours
Step-by-step explanation:
To find the time taken by Joe and Sam together, we have to find the combined work rate of Joe and Sam.
Work rate of Joe is 1 house for 3 hours or (1/3)part of a house in 1 hour. In the same way work rate of Sam is (1/5) part of house per hour.
Time taken by Joe to paint = 3 hours
Part of the house painted in 3 hours = 1
[tex]\sf \text{Part of the house painted by Joe in 1 hour = $\dfrac{1}{3}$}[/tex]
Part of the house painted by Sam in 5 hour = 1
[tex]\sf \text{Part of the house painted by Sam in 1 hour = $\dfrac{1}{5}$}\\\\\sf \text{Part of the house painted by Joe and Sam together in 1 hour = $\dfrac{1}{3} + \dfrac{1}{5}$}[/tex]
[tex]\sf = \dfrac{1*5}{3*5}+\dfrac{1*3}{5*3}\\\\\\=\dfrac{5}{15}+\dfrac{3}{15}\\\\\\=\dfrac{8}{15}[/tex]
[tex]\sf \text{Time taken by Joe and Sam together to paint the house = 1 \div \dfrac{8}{15}}[/tex]
[tex]\sf \text{Time taken by Joe and Sam together to paint the house = $1 \div \dfrac{8}{15}$}[/tex]
[tex]\sf = 1 * \dfrac{15}{8}\\\\= 1.8 \ hours[/tex]
Joe and Sam together have a painting rate of 8/15 of a house per hour. It takes them 1.875 hours to paint a house, which is closest to 1.8 hours. Therefore, the correct answer is b) 1.8 hours.
To solve the problem of how long it will take for Joe and Sam to paint a house together, we can calculate their combined work rate. Joe's rate is one house per three hours, or 1/3 of a house per hour. Sam's rate is one house per five hours, or 1/5 of a house per hour. Together, their combined rate is (1/3 + 1/5) houses per hour.
We find the common denominator, which is 15, and express their combined rate as (5/15 + 3/15) = 8/15 of a house per hour. To find how long it takes to paint the entire house, we take the reciprocal of their combined rate. The reciprocal of 8/15 is 15/8, which represents the total time in hours.
Therefore, 15 divided by 8 gives us 1.875 hours, which means they would take 1 hour and 52.5 minutes (1.875 hours = 1 hour and 52.5 minutes). The closest answer choice to this time is 1.8 hours (simplest exact form), which is answer choice b) 1.8 hours.