Let's first convert the length of the board into inches and then calculate the length of each piece after accounting for the loss per cut.

The length of the board is 5 ft 1 in. There are 12 inches in a foot, so:

5 ft * 12 in/ft = 60 inches

So the total length in inches is:

60 inches 1 inch = 61 inches

Since you're cutting the board into 6 equal pieces, you'll need to make 5 cuts. With a loss of 1/5 inch per cut, the total loss will be:

5 cuts * 1/5 inch/cut = 1 inch

Now, subtract the total loss from the total length of the board:

61 inches - 1 inch = 60 inches

Finally, divide the remaining length by the number of pieces (6) to find the length of each piece:

60 inches / 6 = 10 inches

So each piece will be 10 inches long.