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. Can someone please help me understand this. I know the rational equation would 1/16 + 1/18 + 1/x = 1,but I don't know what to do now

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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. Can someone please help me understand this. I know the rational equation would 1/16 + 1/18 + 1/x = 1,but I don't know what to do now

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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  • phi
I think of these as rate * time = 1 job for example, if you work at a rate of 1 job in 18 hours 1 job/ 18 hours \[ \frac{1}{18} \cdot t= 1 \] and multiply both sides by 18 you get \[ t= 18 \ hours\] just as you should. (that says it will take you 18 hours)
Yes, I get that so far.
  • phi
in your problem, all three working together will take amount "t" \[ \left(\frac{1}{18} + \frac{1}{16}+ \frac{1}{x} \right) t = 1 \]

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  • phi
if we simplify that we get \[ \left( \frac{17}{144} + \frac{1}{x}\right) t = 1 \\ \] if we are told what "t" is , then we can replace t with that number and solve for x
Right, but we don't know what t is...?
So is that all I need to say?
  • phi
the question says *** Explain to Joselyn how this project can tell her how long it would take Charles working alone**** the explanation is we use the time it takes (once we learn what it is) and use that in the above equation to solve for x
Oooooooh!!! NOW I get it!!
  • phi
if you want, we can solve the equation (get x alone on one side) \[ \left( \frac{17}{144} + \frac{1}{x}\right) t = 1 \\ \left( \frac{17}{144} + \frac{1}{x}\right) = \frac{1}{t}\\ \frac{1}{x}= \frac{1}{t}- \frac{17}{144} \\ \frac{1}{x}= \frac{144-17t}{144t} \\ x= \frac{144t}{144-17t} \]
Thank you so so much, I completely understand now!
  • phi
yw

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