15. Josh takes 6 hours to paint a room. Margaret can paint the same room in 4 hours. Assuming their individual rates do not change, how long will it take them to paint the room together?
Answer: B
It will take them 2.4 hours to paint the room together.
When Josh and Margaret work together, their combined rate allows them to complete the room in a shorter amount of time. Specifically, it takes them 2.4 hours to paint the room when their individual painting rates are considered.
A) 1.5 hours
This option is incorrect because it underestimates the time required for Josh and Margaret to complete the task together. To achieve this time frame, they would need to work at an unrealistic combined rate that exceeds their individual capabilities.
B) 2.4 hours
This is the correct answer as it accurately reflects the combined work rate of Josh and Margaret. Their individual rates result in a total time of 2.4 hours when calculated together, making this option valid.
C) 4.8 hours
This option is incorrect because it suggests a time longer than the individual painting rates combined would allow. It does not account for the efficiency gained when both painters work together.
D) 5 hours
This option is also incorrect as it exceeds the calculated time when Josh and Margaret work together. The combined rate would allow them to finish in less time than this option suggests.
E) 10 hours
This option is incorrect as it significantly overestimates the time needed for both individuals to paint the room collaboratively. Their combined efforts will always yield a faster completion time than what is indicated here.
Conclusion
The correct answer, 2.4 hours, is derived from accurately calculating the combined work rates of Josh and Margaret, confirming their efficiency when working together. All other options fail to recognize the productivity gained from their collaboration, resulting in longer completion times that are not feasible based on their individual rates.