A rope 20.6 meters long is cut into two pieces. If the length of one piece of rope is 2.8 meters...

Question

A rope 20.6 meters long is cut into two pieces. If the length of one piece of rope is 2.8 meters shorter than the length of the other, what is the length, in meters, of the longer piece of rope?

GMAT Panda · Accepted Answer

The longer piece measures 11.7 meters. We first create variables to represent the lengths of the two rope pieces. x = length of the longer piece We translate the total length of the rope from the text "A rope 20.6 meters long is cut into two pieces". x + y = 20.6 We translate the relative difference from the text "the length of one piece of rope is 2.8 meters shorter than the length of the other". y = x - 2.8 We substitute the expression for y into the total length equation and solve for x. x + (x - 2.8) = 20.6 2x - 2.8 = 20.6 2x = 20.6 + 2.8 2x = 23.4 x = 11.7

Explanation	Calculations	Help
$We first create variables to represent the lengths of the two rope pieces.$	$x = length of the longer piece$
$We translate the total length of the rope from the text "A rope 20.6 meters long is cut into two pieces" .$	$x + y = 20.6$
$We translate the relative difference from the text "the length of one piece of rope is 2.8 meters shorter than the length of the other" .$	$y = x - 2.8$
$We substitute the expression for y into the total length equation and solve for x .$	$x + (x - 2.8) = 20.6 2 x - 2.8 = 20.6 2 x = 20.6 + 2.8 2 x = 23.4 x = 11.7$

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