Question

if dominik completes a project by himself, it will take him 8 hours. working with katarina, it will take them 5 hours.

	rate (part/hour)	time (hours)	part of project completed
katarina	\\(r\\)	5	\\(5r\\)

if they work together, what is the missing value from the table that represents the part of the project dominik will complete?
\\(\bigcirc\\) \\(8r\\)
\\(\bigcirc\\) \\(8(5)\\)
\\(\bigcirc\\) \\(\frac{1}{8}r\\)
\\(\bigcirc\\) \\(\frac{1}{8}(5)\\)

Explanation:

Step1: Recall Work Rate Formula

The formula for work done is \( \text{Work} = \text{Rate} \times \text{Time} \).

Step2: Apply Formula to Dominik's Work

Dominik's rate is \( \frac{1}{8} \) part/hour and time is 5 hours. So, work done by Dominik is \( \frac{1}{8} \times 5 \), which is \( \frac{1}{8}(5) \).

Answer:

\(\frac{1}{8}(5)\) (the last option)