Let the work could be completed by one man in X days and by one woman in Y days.
From the given information, we can write equations as follows:
1) 6X + 8Y = (1/14) (To complete the work in 14 days, 6 men and 8 women are required)
2) 8X + 12Y = (1/10) (To complete the work in 10 days, 8 men and 12 women are required)
Solving the above equations, we get:
X=16 and Y=21
Therefore, one man can complete the work in 16 days and one woman can complete the work in 21 days.
To find out how much time would be taken to finish the work if only one man or one woman worked alone, we can use the formula:
Total work = (number of workers) x (time taken to finish the work)
Let's calculate the time taken by one man alone:
Total work = 1 (because one man is working alone)
Time taken = (total work) / (work done by one man in one day)
Time taken = 1 / 16 = 0.0625 days (or approximately 1.5 hours)
Similarly, let's calculate the time taken by one woman alone:
Total work = 1 (because one woman is working alone)
Time taken = (total work) / (work done by one woman in one day)
Time taken = 1 / 21 = 0.0476 days (or approximately 1.1 hours)
Thus, it would take approximately 1.5 hours for one man to complete the work alone, and approximately 1.1 hours for one woman to complete the work alone.