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total length of the rope=240 ft

lets get the length of the 1st piece as ''x''

then the length of the second piece =x/2

the length of the 3rd piece =2x

so total length=x+x/2+2x

240=x+x/2+2x

simplify

240=7x/2

480=7x

x=480/7

x=68.57 ft

so the longest length=2x

=2*68.57

=137.14 ft

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