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If it takes three persons to complete a job in 30 hours, how long will it take for one person to complete the same job?

Alexander Gruber
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kripa
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    There are some implied assumptions: that each person is doing equal work, and that the amount of time it takes the complete the job is proportional to the amount of work each person does, so you can view the hours as the unit measuring "work." – trutheality Feb 19 '14 at 16:38
  • Also that the work is being done concurrently by the people. – trutheality Feb 19 '14 at 16:40
  • @trutheality - the common variation is 2 people 20 hours, but person1 take 35 hours alone, how long if just person2 does the work? (or some other numbers, but 2 people working at different levels. – JTP - Apologise to Monica Feb 19 '14 at 16:50
  • @JoeTaxpayer sure, there are many ways to introduce variations, but they need to be explicitly stated. It actually takes some experience with word problems to be able to recognize all the implicit assumptions that are made when those details are not specified. – trutheality Feb 19 '14 at 17:34

2 Answers2

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If one job takes $3$ people $30$ hours, then we can say that

$$ 1(\mathrm{job}) = 3(\mathrm{person}) \cdot 30(\mathrm{hours}) = 90 (\mathrm{person} \cdot \mathrm{hours}). $$

So, if only one person is working, and we wanted to know how long the job would take, we would divide $90 (\mathrm{person} \cdot \mathrm{hours})$ by $1 (\mathrm{person})$.

AnonSubmitter85
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Hints:

Assuming all the workers do the same work in the same time, we have that each man does $\;\frac1{90}$-th of the job in one hour and thus ...

DonAntonio
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