1. **State the problem:** A bicyclist travels 27 miles in 1.5 hours. We need to find the speed in miles per hour (mph). 2. **Formula used:** Speed is calculated by dividing distance by time: $$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$ 3. **Apply the values:** $$\text{Speed} = \frac{27}{1.5}$$ 4. **Simplify the fraction:** $$\text{Speed} = \frac{27}{\cancel{1.5}} \times \frac{\cancel{1}}{1} = 18$$ 5. **Interpretation:** The bicyclist's speed is 18 miles per hour. **Final answer:** The speed is $18$ mph.