34. Josh takes 6 hours to paint a room. Margaret can paint the same room in 4 hours. Assuming that their individual rates do not change, how long will it take Josh and Margaret to paint the room together?
Answer: B
Josh and Margaret will take 2.4 hours to paint the room together.
When working together, Josh and Margaret can complete the painting task in 2.4 hours. This is determined by combining their individual painting rates.
A) 1.5 hours
This option is incorrect because it suggests an unrealistically fast combined rate. Josh's rate is 1 room per 6 hours, and Margaret's is 1 room per 4 hours. Together, they would not be able to complete the room in just 1.5 hours.
B) 2.4 hours
This option is correct. To find the time taken when they work together, we calculate their combined rate: Josh paints at a rate of 1/6 rooms per hour, and Margaret at 1/4 rooms per hour. Their combined rate is (1/6 + 1/4) = 5/12 rooms per hour, leading to a time of 12/5 hours, or 2.4 hours, to complete the room together.
C) 4.8 hours
This option is incorrect as it represents a time longer than the time taken by either person individually. The combined effort of Josh and Margaret should yield a quicker result than the slowest individual rate, which is 6 hours.
D) 5 hours
This choice inaccurately suggests that they would take longer than 4 hours, which is the time it would take for Margaret alone. Since they are working together, the time taken must be less than the slowest individual time.
E) 10 hours
This option is incorrect as it implies an extended time for completion, which does not reflect the efficiency of combining their efforts. Given their individual rates, they are capable of painting the room significantly faster than 10 hours.
Conclusion
The correct answer, 2.4 hours, reflects the effective collaboration between Josh and Margaret, where their combined painting rates result in a shorter completion time. All other options fail to accurately represent the combined efficiency achieved through teamwork in this scenario.