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anonymous
 one year ago
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
anonymous
 one year ago
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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phi
 one year ago
Best ResponseYou've already chosen the best response.1I 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)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, I get that so far.

phi
 one year ago
Best ResponseYou've already chosen the best response.1in your problem, all three working together will take amount "t" \[ \left(\frac{1}{18} + \frac{1}{16}+ \frac{1}{x} \right) t = 1 \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1if 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Right, but we don't know what t is...?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So is that all I need to say?

phi
 one year ago
Best ResponseYou've already chosen the best response.1the 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oooooooh!!! NOW I get it!!

phi
 one year ago
Best ResponseYou've already chosen the best response.1if you want, we can solve the equation (get x alone on one side) \[ \left( \frac{17}{144} + \frac{1}{x}\right) t = 1 \\ \left( \frac{17}{144} + \frac{1}{x}\right) = \frac{1}{t}\\ \frac{1}{x}= \frac{1}{t} \frac{17}{144} \\ \frac{1}{x}= \frac{14417t}{144t} \\ x= \frac{144t}{14417t} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so so much, I completely understand now!
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