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Question

If m workers can do a job in d days, how long would it take 40 workers to do the same job?

Solution

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This rate problem has four variables: rate, number of workers, length of time, and number of jobs:

rate×workers×time=jobs\text{rate}\times\text{workers}\times \text{time}=\text{jobs}

RWT=JRWT=J

Solve for the rate, RR, for W=m,T=d,W=m,T=d, and J=1J=1:

R(m)(d)=1R(m)(d) =1

R=1mdjobworker-daysR =\dfrac{1}{md}\dfrac{\text{job}}{\text{worker-days}}

Solve for TT using R=1md,W=40,R=\dfrac{1}{md}, W=40, and J=1J=1 (same job):

T=11md40T=\dfrac{1}{\dfrac{1}{md}\cdot 40}

T=md40 days\color{#c34632}{T=\dfrac{md}{40}\text{ days}}

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