If Judy completes a puzzle by herself, it takes her 3 hours. Working with Sal, it only takes them 2 hours.

\begin{tabular}{|c|c|c|c|}
\hline
& \begin{tabular}{c}
Rate \\
(parts/hour)
\end{tabular}
& \begin{tabular}{c}
Time \\
(hours)
\end{tabular}
& \begin{tabular}{c}
Part of \\
Project \\
Completed
\end{tabular} \\
\hline
Judy
& [tex]$?$[/tex]
& 2
& [tex]$\frac{2}{3}$[/tex] \\
\hline
Sal
& [tex]$r$[/tex]
& 2
& [tex]$2 r$[/tex] \\
\hline
\end{tabular}

What is the missing value from the table that represents Judy's rate?

A. [tex]$r$[/tex]

B. [tex]$3-r$[/tex]

C. [tex]$\frac{1}{3}$[/tex]

D. 3



Answer :

To find the missing value from the table that represents Judy's rate, we need to determine the rate at which she completes the puzzle per hour.

1. Determine the time it takes for Judy to complete the puzzle on her own:
- It takes Judy 3 hours to complete the entire puzzle by herself. Therefore, in 1 hour, she completes [tex]\( \frac{1}{3} \)[/tex] of the puzzle.

2. Use this information to determine her rate:
- Her rate of work is parts of the puzzle per hour, which is [tex]\( \frac{1}{3} \)[/tex].

3. Fill in the Table:
- Judy's rate is [tex]\( \frac{1}{3} \)[/tex]
- Judy works for 2 hours
- So, the part of the project she completes in 2 hours is [tex]\( 2 \times \frac{1}{3} = \frac{2}{3} \)[/tex]

So, Judy's rate is [tex]\( \frac{1}{3} \)[/tex] parts of the puzzle per hour.

The missing value from the table that represents Judy's rate is:
[tex]\[ \frac{1}{3} \][/tex]