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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:

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

$RWT=J$

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

$R(m)(d) =1$

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

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

$T=\dfrac{1}{\dfrac{1}{md}\cdot 40}$

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

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