Final answer:
Using the rates at which two men can mow a field, it is calculated that together, working alternately with one beginning at 9 am, the mowing will be finished at 7:50 pm.
Step-by-step explanation:
Let's start by calculating the work rate of each man. Man A can complete the mowing in 10 hours, which means he mows at the rate of 1/10 of the field per hour. Man B mows at a rate of 1/12 of the field per hour. When they work alternately, we need to find out how much of the field is mowed after each segment of two hours (since each man works for one hour and then the other takes over).
In the first two-hour segment, A works for the first hour, and B works for the second hour. So, the field mowed is:
1/10 (by A in the first hour) + 1/12 (by B in the second hour)
= 6/60 + 5/60
= 11/60
This means they mow 11/60 of the field in two hours working alternately. To mow the entire field, we divide the total work (1, i.e., the whole field) by the work done in two hours:
1 / (11/60) = 60/11 ≈ 5.45 two-hour segments.
Since 5.45 is not a whole number, they will complete 5 full segments and will need a part of the sixth segment to finish mowing the field. Five full segments take 5*2 = 10 hours. Now we need to calculate how much of the field is left after 5 segments (10 hours):
5 * (11/60) = 55/60 = 11/12 of the field is mowed.
The remaining 1/12 of the field will be mowed by A (since he starts the next segment). Since A mows at a rate of 1/10 per hour, he will need:
1/12 field * 10 hours/field = 10/12 hours = 50 minutes to finish the remaining part.
Therefore, the mowing will be finished at:
9 am + 10 hours + 50 minutes = 7:50 pm.