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?

Rationale

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

When working together, Josh and Margaret's combined work rates can be calculated to determine the total time they will need to paint the room. Josh’s rate is 1/6 of the room per hour, while Margaret’s rate is 1/4 of the room per hour. Their combined rate is 1/6 + 1/4 = 5/12 of the room per hour, leading to a total time of 12/5 hours, which equals 2.4 hours.

A (1.5 hours) YOUR ANSWER

This option suggests that they can complete the task in 1.5 hours, which implies a combined work rate of 2/3 of the room per hour. However, this rate exceeds their actual combined work rate of 5/12, making this option incorrect.

B (2.4 hours) CORRECT

This is the correct answer as it accurately reflects the time taken when combining their work rates. The combined rate of Josh and Margaret is 5/12 of the room per hour, leading to a total time of 2.4 hours to paint the room together.

C (4.8 hours) YOUR ANSWER

This choice implies a slower combined work rate, suggesting that they would take longer than necessary. A combined time of 4.8 hours indicates a work rate of 1/4.8, which does not account for the efficiency gained by working together.

D (5 hours) YOUR ANSWER

Choosing 5 hours would imply a combined rate that is slower than either individual rate, which is not possible. The combined effort of both painters should result in a faster completion time than either could achieve alone.

E (10 hours) YOUR ANSWER

This option indicates an exceedingly slow combined rate that does not reflect their individual capabilities. Since both can paint the room significantly faster on their own, a combined time of 10 hours is unrealistic.

Conclusion

The collaborative effort of Josh and Margaret leads to a total painting time of 2.4 hours, calculated through their combined work rates. Each incorrect option misrepresents their efficiency when working together, demonstrating the importance of understanding rates in collaborative tasks.