Question

working together, alex and millie can file all the papers in the file cabinets in 4 hours. it would have taken alex 6 hours to do the job alone. what is the missing value in the table that represents the part of the papers that alex would file if alex and millie worked together?

	rate (part/hour)	time (hours)	part of papers filed
millie	( r )	4	( 4r )

options: ( \frac{4}{6} ), ( 4r ), ( \frac{6}{4} ), ( 6r )

Explanation:

Step1: Determine Alex's rate

Alex can do the job alone in 6 hours. So his rate (part per hour) is $\frac{1}{6}$ (since work = rate × time, and total work is 1 job, so rate = $\frac{1}{time}$).

Step2: Calculate part of papers Alex filed

When working together, the time Alex works is 4 hours. The part of the job done by Alex is rate × time. So Alex's rate is $\frac{1}{6}$ and time is 4 hours, so the part is $\frac{1}{6}×4=\frac{4}{6}$.

Answer:

$\frac{4}{6}$