If one piece is 5 ft longer than the other, we subtract 5 from 100 and get 95 feet. This is twice the length of the shorter piece so its length must be half of 95=47½ feet, and the longer piece is 52½ feet.

We can do this by algebra: let x be the length of the shorter piece, then x+5 is the length of the other, so their combined lengths are x+x+5=100, 2x+5=100, 2x=95, x=47½ and x+5=52½ feet.

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