If John can do a job (which is digging a ten foot ditch) alone in 4 hours and Michael can do the same job alone in 8 hours, it makes no sense for them working together to do the same job in 6 hours. Keep in mind that if Michael just sits aside and watches John instead of helping, the job will be done in 4 hours, so unless Michael makes things harder for John instead of helping him, there is no way they will finish the job in more than 4 hours if they are working together. As Michael will be helping John, we expect the job to be finished in less than 4 hours.

To find the amount of time when John and Michael are working together, just note how much of the job each person can do in one hour: John finishes 1/4 of the job in one hour, and Michael finishes 1/8 of the job in one hour. When they work together, 1/4 + 1/8 = 3/8 of the job gets done in one hour; thus, the whole job will be completed in 1/(3/8) = 8/3 hours, which is roughly 2.67 hours.

To solve the question, first I assume that you meant to write M + K instead of M + M. Using the same logic as above, John and Luke working together will complete 1/4 + 1/6 = 5/12 of the job in one hour, so it will take the two 1/(5/12) = 12/5 = 2.4 hours. Michael and Kevin can complete 1/5 + 1/8 = 13/40 of the job in one hour, so it will take the two 1/(13/40) = 40/13 hours, which is roughly 3.08 hours. So, it takes Michael and Kevin longer than John and Luke to finish the same job.

Note: If the question actually wanted us to compare the time for other couples, you can calculate the couples’ time just the same way as I did above.