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?

Answer: Approximately 4 hours and 27 minutes.

Explanation: Let Officer Kay's hours be represented by 1/8

and Officer Ming's hours be represented by 1/10.

That means that Officer Kay completes 1/8 of the job in 1 hour and Officer Ming completes 1/10 of the job in 1 hour.

If they work together,

It would be 1/8 + 1/10 =

Finding the LCM of the denominator, which is 80,

Addition of 1/8 and 1/10 is 9/40.

Let T be 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 = 40/9 = 4.444 or 4 and 4/9.

Converting 4.444 to hours and minutes, we have 4 hours 27 minutes.

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.