Question

Joselyn is a manager at a sign painting company. She has three painters, Allen, Brianne, and Charles. Allen can complete a large project in 16 hours. Brianne can complete the same sized project in 18 hours. Charles is new, so no one knows how long it will take him.

Joselyn assigns them all a large project to complete together. Explain to Joselyn how this project can tell her how long it would take Charles if he worked by himself. Use complete sentences.

Answer 1

This is what I have so far:
Allen can complete 1/16 of the project per hour
Brianne can complete 1/18 of the project per hour
Charles can complete 1/x

Together they can accomplish 1/16 + 1/18 + 1/X per hour.
We need a common denominator to get rid of all the fractions which is 144x.

Answer 2

I don't think I have the full equation and am unsure how to proceed, anyone wanna help?

Answer 3

lol everyone hates these word problems
i am sure we can do it, give me a moment to look carefully

Answer 4

actually it looks like you are doing well on your own

Answer 5

I was, and then I confused the heck out of myself and now im really confused

Answer 6

their combined rate is
\[\frac{1}{16}+\frac{1}{18}+\frac{1}{x}\] \[=\frac{144+17x}{144x}\]

Answer 7

now suppose it takes them \(5\) hours to do it together
that means \[5\times \left(\frac{144+117x}{144x}\right)=1\]
rate times time equals one job

Answer 8

actually i think i made it more complicated
no matter, we can fix it
keeping with my example of \(5\) hours that means
\[\frac{144+17x}{144x}=\frac{1}{5}\] and you can solve that for \(x\) by
\[5(144+17x)=144x\]

Answer 9

now replace \(5\) by some variable for time of your choice, and explain that in complete sentences

Answer 10

okay, that makes sense, thanks!