A 256m long rope was cut into two parts, one of which is 7 times longer than the other.

A 256m long rope was cut into two parts, one of which is 7 times longer than the other. How many meters is one part of the rope longer than the other?

1) Let the length of the smaller part of the rope be x (x) m, then the second part has a length: (x · 7) meters. Knowing the original length of the entire rope, we create the equation:

x + x * 7 = 256;

x 8 = 256;

x = 256: 8;

x = 32 (m) – the length of the first (smaller) part of the rope.

2) Determine the length of the second part of the rope: x · 7 = 32 · 7 = 224 (m).

3) Find out how many meters one part of the rope is longer than the second part: 224 – 32 = 192 (m).

Answer: one part is 192 m longer than the second part.