Final answer:
When Alex and JP work together for one hour and then JP works alone for the next hour, they complete ⅞ of the job. The remaining ⅚ of the job would take JP 2 hours to complete, which simplifies to 1 hour and 60 minutes. However, none of the provided answer choices correctly match this solution. So the correct answer is option D.
Step-by-step explanation:
To solve the question, we need to first find out how much of the job Alex and JP can complete in one hour when working together. Since Alex can do the job in 3 hours, his work rate is ⅓ of the job per hour. Similarly, JP's work rate is ¼ of the job per hour. When working together for one hour, they complete ⅓ + ¼ = ⅜ of the job.
Since only JP worked in the second hour, he completed another ¼ of the job. By the end of the second hour, JP and Alex together have completed ⅜ + ¼ = ⅞ of the job.
To find out how much is left to do, we subtract ⅞ from the whole job, which is 1 - ⅞ = ⅚. JP, working alone, needs to complete this remaining ⅚ of the job. Since his work rate is ¼ per hour, we divide ⅚ by ¼ to find the time JP needs, which equals ⅚ ÷ 4 = 2 hours, or 1 hour and 60 minutes. Therefore, the remaining time that JP takes to finish the job is 1 hour and 60 minutes, which simplifies to 2 hours.
However, the option closest to 2 hours in the provided choices is 1 hour and 40 minutes (B), which suggests a possibility of a mistake in the question or the choices. Assuming no errors, none of the provided answer choices A, B, C, or E correctly represents the correct total time for JP to finish the remaining job. If '1 hour and 60 minutes' or '2 hours' were listed as an option, that would have been the correct answer.