Dinesh has been keeping track of his time at work over the past month. Answer the question below using the information in the table.

\begin{tabular}{|c|c|c|c|c|c|}
\hline
\multicolumn{6}{|c|}{Dinesh's Time in Hours} \\
\hline
& Meetings & Design & Deliverables & Worked \\
\hline
Week 1 & [tex]$7\frac{1}{4}$[/tex] & [tex]$4\frac{1}{4}$[/tex] & [tex]$23\frac{1}{3}$[/tex] & 22.3 \\
\hline
Week 2 & 42.3 & [tex]$24\frac{1}{7}$[/tex] & [tex]$16\frac{1}{3}$[/tex] & [tex]$12\frac{1}{2}$[/tex] \\
\hline
Week 3 & 3.50 & 3.83 & 9.33 & 19.33 \\
\hline
Week 4 & 6.17 & 3.40 & 4.20 & 20.80 \\
\hline
\end{tabular}

How many hours did he work in Week 2?

A. [tex]$\frac{361}{14}$[/tex]
B. [tex]$\frac{358}{14}$[/tex]
C. [tex]$\frac{368}{15}$[/tex]
D. [tex]$35\frac{1}{14}$[/tex]



Answer :

To determine how many hours Dinesh worked in Week 2, we need to sum up all the hours he spent in different activities during that week. Let's examine each component given in Week 2 and then find their total.

1. Meetings: The time spent in meetings during Week 2 is 423 hours.

2. Design:
- The given time for design is [tex]\( \frac{24}{7} \)[/tex] hours.
- This can be directly read as the provided result: 3.4285714285714284 hours.

3. Deliverables:
- The given time for deliverables is [tex]\( \frac{161}{3} \)[/tex].
- This can be directly read as the provided result: 53.666666666666664 hours.

4. Worked:
- The given time for working on generic tasks is [tex]\( \frac{121}{2} \)[/tex].
- This can be directly read as the provided result: 60.5 hours.

Now, we add up all these components to find the total time Dinesh worked in Week 2:

[tex]\[ 423 \, \text{(Meetings)} + 3.4285714285714284 \, \text{(Design)} + 53.666666666666664 \, \text{(Deliverables)} + 60.5 \, \text{(Worked)} = 540.5952380952381 \text{ hours} \][/tex]

Therefore, the total number of hours Dinesh worked in Week 2 is approximately 540.595 hours. This does not correspond exactly to any of the answer choices provided in the question (a, b, c, d). The likely reason is either a possible error in the question setup or a mismatch in options.

Thus, for precision:
- The correct total number of hours Dinesh worked in Week 2 is 540.5952380952381 hours.