1. **State the problem:** We have a racetrack made of 25 equal pieces, and the total length is 150 inches. We want to find the length $p$ of each piece. 2. **Identify the correct equation:** Since the total length is the sum of all pieces, and each piece is length $p$, the equation is: $$25p = 150$$ The other equation $\frac{p}{25} = 150$ does not model the problem correctly. 3. **Solve the equation:** Divide both sides by 25 to isolate $p$: $$\cancel{25}p = \frac{150}{\cancel{25}}$$ Simplify the right side: $$p = 6$$ 4. **Interpret the result:** Each piece of the racetrack is 6 inches long. **Final answer:** $$p = 6 \text{ inches}$$