Final answer:
After 1 hour of working together, Machine A and Machine B complete 5/6 of the job. Machine B breaks down, and Machine A alone takes an additional 1/3 hour to finish the remaining 1/6 of the job. None of the provided options are correct.
Step-by-step explanation:
Machine A takes 2 hours to paint a car alone, and Machine B takes 3 hours to paint a car alone. To figure out how much work each machine does per hour, we calculate their rates of work. Machine A's rate is 1/2 car per hour, and Machine B's rate is 1/3 car per hour. When they work together, they can paint 1/2 + 1/3 = 3/6 + 2/6 = 5/6 cars per hour. After working together for 1 hour, they complete 5/6 of the job, leaving 1/6 of the job unfinished.
Now, we need to calculate how much longer it will take for Machine A to finish the remaining 1/6 of the job alone. Since Machine A's rate is 1/2 car per hour, it will take Machine A 1/6 divided by 1/2, which equals 1/6 * 2/1 = 2/6 = 1/3 hour to finish the job. Therefore, it will take Machine A an additional 1/3 hour to finish painting the car on its own after Machine B breaks down. To answer the question, none of the options (A) 1 hour, (B) 2 hours, (C) 3 hours, (D) 4 hours accurately reflect the calculated time of 1/3 hour.