While working the evening shift, Agent K took 8 hours to complete a task and Agent M took 10 hours to complete the same type of task. How many hours would it take Agent K and Agent M to complete the same task working together, each working at his own rate?

Question

Quizplus · Accepted Answer

Let Agent K's hours be represented by 1/8 and Agent M's hours be represented by 1/10. This says that Agent K completes 1/8 of the job per hour and Agent M completes 1/10 of the job per hour. Together, they work 1/8 + 1/10 = 18/80 of the job per hour, which when reduced to its lowest terms, is 9/40. Therefore, if T is the amount of time it takes the two of them to finish the job, then 9/40 of the job per hour x T (hours) has to equal 1 job. So, 9/40 x T = 1 and T = 40/9 = 4 4/9 hours (four and four-ninths hours).

While Working the Evening Shift, Agent K Took 8 Hours