Question

12 people can wash 40 cars in 12 days. how many days will it take 4 people to wash 30 cars

Answer 1

First off, let's keep in mind we're looking for "days worth", how many days does it take to do an amount of cars.

so 12 folks can do in 12 days 40 cars, since each person is working every one of those 12 days, then each of those persons is working 12 days, now, there are 12 folks, that means the combined amount of days will be 12+12+12+12+12+12+12+12+12+12+12+12, or 12*12, 144 days worth, it takes them to do 40 cars.

so, to the same folks, how many days will it take them to do 30 cars?

$\bf \stackrel{12~folks}{\begin{array}{ccll} days&cars\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 144&40\\ x&30 \end{array}}\implies \cfrac{144}{x}=\cfrac{40}{30}\implies \cfrac{144\cdot 30}{40}=x\implies 108=x$

that's 108 days worth for doing 30 cars.

for 12 folks, that'd be 108/12 or 9 days, 12 folks can do it in 9 days.

what about 4 folks only?  108/4 or 27 days.