1. **State the problem:** Calculate the new hourly rate given the number of hours worked per week and the new weekly earnings. 2. **Given data:** - Hours worked per week: $25.5$ hours - New weekly earnings: $301.75$ 3. **Formula used:** Hourly rate $= \frac{\text{Weekly earnings}}{\text{Hours worked}}$ 4. **Calculate the new hourly rate:** $$\text{Hourly rate} = \frac{301.75}{25.5}$$ 5. **Intermediate step showing division:** $$\text{Hourly rate} = \frac{\cancel{301.75}}{\cancel{25.5}}$$ 6. **Perform the division:** $$\text{Hourly rate} = 11.83$$ 7. **Answer:** Her new hourly rate is **11.83** per hour.