If 15 oxen or 20 cows can eat the grass of a field in 80 days, then in how many days will 6 oxen and 2 cows eat the same grass?

Sure, let's solve this step by step:

Step 1: First, we need to find out the amount of grass a single ox or cow can eat in a day. According to the problem, 15 oxen can eat the grass of a field in 80 days. So, one ox will eat the same amount of grass in 1580 = 1200 days. Similarly, one cow will eat the same amount of grass in 2080 = 1600 days.

Step 2: Now, we need to find out the amount of grass 6 oxen and 2 cows can eat in a day. So, 6 oxen will eat the amount of grass in 1200/6 = 200 days and 2 cows will eat the same amount of grass in 1600/2 = 800 days.

Step 3: Since the 6 oxen and 2 cows are eating the grass together, we need to find out how many days they will take to eat the grass of the field. We can do this by finding the harmonic mean of the two values. The formula for the harmonic mean of two values is 2ab/(a+b). So, the harmonic mean of 200 and 800 is 2200800/(200+800) = 285.71 days.

So, 6 oxen and 2 cows will eat the grass of the field in approximately 286 days.