Write an equation as part of solving the problem. The operating speed of a personal computer is 50 gigahertz. This is one-fourth the speed of a newer model. Find the speed of the newer personal computer.

Let's denote the speed of the newer personal computer as \(x\) gigahertz. According to the problem, the operating speed of the older personal computer is \(50\) gigahertz, and this is one-fourth the speed of the newer model. Mathematically, we can represent this relationship as: \[\frac{1}{4} \times x = 50\] Now, we solve for \(x\), the speed of the newer personal computer: \[\frac{1}{4} \times x = 50\] To isolate \(x\), we multiply both sides of the equation by \(4\): \[x = 4 \times 50\] \[x = 200\] So, the speed of the newer personal computer is \(200\) gigahertz.