1. **Problem statement:** A nurse takes 12 minutes to reach the hospital traveling at 5 miles per hour. We want to find how long she would take if she cycled at 15 miles per hour. 2. **Formula used:** Time = Distance \div Speed. 3. **Step 1:** Calculate the distance to the hospital using the original speed and time. Convert 12 minutes to hours: $$12 \text{ minutes} = \frac{12}{60} = 0.2 \text{ hours}$$ Distance = Speed \times Time = $$5 \times 0.2 = 1 \text{ mile}$$ 4. **Step 2:** Calculate the new time taken at 15 miles per hour. Time = Distance \div Speed = $$\frac{1}{15} = 0.0667 \text{ hours}$$ 5. **Step 3:** Convert the time back to minutes. $$0.0667 \times 60 = 4 \text{ minutes}$$ **Final answer:** She would take 4 minutes if she cycled at 15 miles per hour.