To determine how many minutes John Jr. and John Sr. together will take to construct 600 boxes, let's first figure out their individual production rates and then their combined production rate.
1. John Jr.’s construction rate:
- John Jr. constructs 180 boxes per hour.
- Since there are 60 minutes in an hour, his rate per minute is:
[tex]\[
\text{John Jr.'s rate per minute} = \frac{180 \text{ boxes}}{60 \text{ minutes}} = 3 \text{ boxes per minute}
\][/tex]
2. John Sr.’s construction rate:
- John Sr. constructs 20 boxes per hour.
- Similarly, his rate per minute is:
[tex]\[
\text{John Sr.'s rate per minute} = \frac{20 \text{ boxes}}{60 \text{ minutes}} \approx 0.333 \text{ boxes per minute}
\][/tex]
3. Combined construction rate:
- Together, their combined rate is the sum of their individual rates:
[tex]\[
\text{Combined rate} = 3 \text{ boxes per minute (John Jr.)} + 0.333 \text{ boxes per minute (John Sr.)} \approx 3.333 \text{ boxes per minute}
\][/tex]
4. Total time needed to construct 600 boxes:
- To find the total time in minutes, divide the total number of boxes by their combined rate:
[tex]\[
\text{Time needed} = \frac{600 \text{ boxes}}{3.333 \text{ boxes per minute}} = 180 \text{ minutes}
\][/tex]
Therefore, John Jr. and John Sr. together will take 180 minutes to construct 600 boxes, thus the answer is:
[tex]\[
\boxed{180}
\][/tex]
