While working the evening shift, Officer Kay took 8 hours to complete a task at her work station and Officer Ming took 10 hours to complete the same task at his work station. How many hours would it take Officer Kay and Officer Ming to complete the same task working together, each working at their own work station?

Question

Quizplus · Accepted Answer

Let Officer Kay's hours be represented by 1/8 and Officer Ming's hours be represented by 1/10. This reframes the data, indicating that Officer Kay completes 1/8 of the job per hour and Officer Ming 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 x T (expressed in hours) has to equal 1 job. So, (9/40) x T = 1, therefore T= 1/(9/40), or T = 40/9. This means it would take 4 and 4/9 hours (about 4 hours and 27 minutes) for Officers Kay and Ming to complete the task together.

While Working the Evening Shift, Officer Kay Took 8 Hours