Answer
The cut should be made at 0.80 of the way along the wire (or, equivalently, at 0.20 of the way).
Work Step by Step
Equation 18-3 shows that the resistance is directly proportional to the length of the wire. The length of the longer, higher-resistance piece should be 4.0 times the length of the shorter, lower-resistance piece.
Make the cut at 0.80 of the way along the wire (or, equivalently, at 0.20 of the way).
The resistance of the longer piece is $0.8 \times 15.0\Omega = 12.0\Omega$, and that of the shorter piece is $0.2 \times 15.0\Omega = 3.0\Omega$.
The sum of the resistances of the two wires in series is the original $15.0\Omega$.
