A rectangular plot of private property is fenced in by a chain-link fence. The long sides of the plot are three times the length of the short sides. One short side of the fence is rusted from being hit by a sprinkler and needs to be replaced. If all the sides of the fence together are 640 feet long, how many feet of fence need to be replaced? Give me reasons, before answering the question
Let S be the length of the short side of the fence. Thus, the length of a long side of the fence is 3S. There are 2 of each side, so the whole fence is 2S + 2 * 3S = 2S + 6S = 8S long. The whole fence is 8S = 640 feet long. Thus, the short side of the fence that needs to be replaced is S = 640 / 8 = 80 feet long. So the final answer is 80.