1. **State the problem:** Megan rode a penny-farthing where the big wheel has radius 36 units and made 9 complete rotations. The small wheel has radius 12 units. We need to find: a) The distance Megan rode. b) The number of complete rotations the small wheel made. 2. **Formula for distance traveled by a wheel:** The distance traveled by a wheel after one complete rotation is the circumference of the wheel, given by: $$\text{Circumference} = 2\pi r$$ where $r$ is the radius of the wheel. 3. **Calculate distance Megan rode:** - Radius of big wheel $r_b = 36$ - Number of rotations $n_b = 9$ Distance traveled by big wheel: $$\text{Distance} = n_b \times 2\pi r_b = 9 \times 2\pi \times 36$$ Calculate: $$= 9 \times 72\pi = 648\pi$$ Approximate using $\pi \approx 3.1416$: $$648 \times 3.1416 = 2036.7$$ So, Megan rode approximately **2036.7 units**. 4. **Calculate rotations of the small wheel:** - Radius of small wheel $r_s = 12$ - Distance traveled is the same for both wheels. Number of rotations of small wheel $n_s$: $$n_s = \frac{\text{Distance}}{\text{Circumference of small wheel}} = \frac{648\pi}{2\pi \times 12}$$ Simplify: $$= \frac{\cancel{648}\pi}{2\pi \times \cancel{12}} = \frac{648}{24} = 27$$ So, the small wheel made **27 complete rotations**. **Final answers:** - a) Distance Megan rode: **2036.7 units** (to 1 decimal place) - b) Small wheel rotations: **27**