1. **State the problem:** Lina is driving at 46 mph and accelerates to 51 mph while overtaking a lorry. We need to calculate the percentage increase in her speed. 2. **Formula for percentage increase:** $$\text{Percentage increase} = \left(\frac{\text{New value} - \text{Original value}}{\text{Original value}}\right) \times 100\%$$ 3. **Apply the values:** $$\text{Percentage increase} = \left(\frac{51 - 46}{46}\right) \times 100\%$$ 4. **Calculate the difference:** $$51 - 46 = 5$$ 5. **Substitute the difference:** $$\text{Percentage increase} = \left(\frac{5}{46}\right) \times 100\%$$ 6. **Simplify the fraction:** $$\text{Percentage increase} = \left(\frac{\cancel{5}}{\cancel{46}}\right) \times 100\% = \frac{5}{46} \times 100\%$$ 7. **Calculate the decimal:** $$\frac{5}{46} \approx 0.1087$$ 8. **Convert to percentage:** $$0.1087 \times 100\% = 10.87\%$$ 9. **Final answer:** The percentage increase in Lina's speed is approximately **10.87%**.