Answer: C - 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.
