A steel rod that is 64 feet long must be cut into three pieces to fabricate the supports for a drill press. The longest piece is 3.09 times the shortest and the middle piece is 1.73 times the shortest. How long is each piece? Round nearest foot.

let's x be the shortest piece

the middle piece is 1,73 * x

the longest piece is 3,09 x

then if we sum the 3 pieces we will get the steel rod that is 64 feet long

so x+1,73x+3,09x = 5,82x = 64 then x = 10,99 = 11

the shortest piece is 11 feet

the middle piece is 1,73*11=19,03 feet

The longest piece is: 3,09*11 = 33,99 = 34 feet