Machine A can complete a job in 8 hours, and Machine B can complete the same job in 12 hours. If both machines work together, how many hours will they take to complete the job?
Answer: 4.8 hours
Explanation
Machine A can complete the job in 8 hours, so its work rate is 1/8 of the job per hour.
Machine B can complete the job in 12 hours, so its work rate is 1/12 of the job per hour.
When they work together, their combined work rate is the sum of their individual work rates:
(1/8 + 1/12) of the job per hour
To add these fractions, we need a common denominator, which is 24. So we get:
(3/24 + 2/24) = 5/24 of the job per hour
Since they can complete 5/24 of the job in 1 hour, they can complete the entire job (1) in:
24/5 = 4.8 hours
So, the correct answer is: 4.8 hours!
