To determine the shortest length of board the carpenter can buy, we need to calculate the total length of board needed to cut four sections, each 3 feet 8 inches long.
First, we need to convert 3 feet 8 inches to inches:
3 feet x 12 inches per foot = 36 inches
8 inches = 8 inches
Total length of one section = 36 + 8 = 44 inches
To cut four sections, the total length of board needed is:
4 sections x 44 inches per section = 176 inches
Since the board is only sold by the foot, we need to convert 176 inches to feet:
176 inches ÷ 12 inches per foot = 14.67 feet
Therefore, the carpenter needs to buy at least 14.67 feet of board to cut four sections, each 3-feet 8-inches long. Since she can only buy whole feet of board, she will need to round up to the nearest foot. Therefore, the shortest length of board she can buy is 15 feet.