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?

Rationale

Josh and Margaret will take 2.4 hours to paint the room together.

To solve this problem, we can determine their individual painting rates and then combine them to find the total time taken when they work together. Josh paints at a rate of 1/6 rooms per hour, while Margaret paints at a rate of 1/4 rooms per hour. When combined, their rates add up to 5/12 rooms per hour, leading to a total time of 2.4 hours to complete one room.

A (1.5 hours) YOUR ANSWER

This choice is incorrect as it suggests an unrealistically short time frame for both individuals. If Josh and Margaret worked together, their combined rate would not allow them to finish the room in 1.5 hours, as calculated from their individual rates.

B (2.4 hours) CORRECT

This is the correct answer. Combining their rates (1/6 + 1/4 = 5/12) results in a total painting time of 2.4 hours for the room when both work simultaneously.

C (4.8 hours) YOUR ANSWER

This option is incorrect because it exceeds the time calculated when both individuals are working together. The combined rate is efficient enough to reduce the time needed to less than 4.8 hours.

D (5 hours) YOUR ANSWER

This choice is also incorrect; although it reflects a reduction from the initial individual times, it remains too long compared to the effective combined rate they achieve while painting together.

E (10 hours) YOUR ANSWER

This option is incorrect as it implies a significantly longer time than either individual would take alone. The combined efficiency of both Josh and Margaret guarantees that they complete the task far quicker than 10 hours.

Conclusion

When working together, Josh and Margaret can complete the painting task in 2.4 hours due to the synergy of their individual painting rates. By calculating their combined rate accurately, we see that they are much more efficient working as a team than individually, confirming that collaborative effort can significantly enhance productivity.