Final answer:
One man and one woman together will take 2/3 day (or approximately 0.67 day) to complete the same work.
Step-by-step explanation:
To find out how many days it will take for one man and one woman to complete the work together, we need to calculate the combined efficiency of one man and one woman.
From the given information, we know that one man can finish the work in 39 days and two women can also finish the work in 39 days. This means that one man's work is equivalent to two women's work. So, if we consider one man's work as 1 unit, then one woman's work is 1/2 unit. Therefore, the combined work of one man and one woman is 1 unit + 1/2 unit = 3/2 units.
Now, let's calculate how many days it will take for them to complete the work together. Since they are working together, their combined efficiency is 1 + 1/2 = 3/2 units per day. To find the number of days required, we divide the total work (1 unit) by their combined efficiency (3/2 units per day): 1 / (3/2) = 2/3 day.
Therefore, one man and one woman together will take 2/3 day (or approximately 0.67 day) to complete the same work.