1. **State the problem:** We need to find the average speed of a bus that travels 36 miles in 1 hour and 30 minutes. 2. **Formula used:** Average speed is calculated by dividing the total distance traveled by the total time taken. $$\text{Average speed} = \frac{\text{Distance}}{\text{Time}}$$ 3. **Convert time to hours:** 1 hour and 30 minutes is equal to 1.5 hours. 4. **Calculate average speed:** $$\text{Average speed} = \frac{36}{1.5}$$ 5. **Simplify the fraction:** $$\text{Average speed} = \frac{36}{\cancel{1.5}} \times \frac{\cancel{1}}{1} = 24$$ 6. **Final answer:** The average speed of the bus is **24 miles per hour**.