Question

it takes kim 13 minutes to sweep a porch. mei can sweep the same porch in 14 minutes. find how long it would take them if they worked together. minutes = 6 seconds =

Explanation:

Step1: Calculate work - rates

Kim's rate of work is $\frac{1}{13}$ of the porch per minute (since she takes 13 minutes to sweep the porch). Mei's rate of work is $\frac{1}{14}$ of the porch per minute (since she takes 14 minutes to sweep the porch).

Step2: Find combined rate

The combined rate of Kim and Mei working together is $\frac{1}{13}+\frac{1}{14}=\frac{14 + 13}{13\times14}=\frac{27}{182}$ of the porch per minute.

Step3: Calculate time taken together

Let $t$ be the time taken when they work together. Since rate $\times$ time = work (and work = 1 porch), we have $t=\frac{1}{\frac{27}{182}}=\frac{182}{27}$ minutes.

Step4: Convert to minutes and seconds

$\frac{182}{27}=6\frac{20}{27}$ minutes. The fractional part $\frac{20}{27}$ of a minute is $\frac{20}{27}\times60=\frac{1200}{27}\approx44.44$ seconds. Rounding to the nearest second, we get 44 seconds.

Answer:

Minutes = 6, Seconds = 44