1. **Convert 5 yards per minute to feet per hour.** 2. Start with the given rate: $5 \frac{\text{yd}}{\text{min}}$. 3. Use the conversion $1 \text{ yd} = 3 \text{ ft}$ to convert yards to feet: $$5 \frac{\text{yd}}{\text{min}} \times \frac{3 \text{ ft}}{1 \text{ yd}} = 15 \frac{\text{ft}}{\text{min}}$$ 4. Convert minutes to hours using $1 \text{ hr} = 60 \text{ min}$: $$15 \frac{\text{ft}}{\text{min}} \times \frac{60 \text{ min}}{1 \text{ hr}} = 900 \frac{\text{ft}}{\text{hr}}$$ 5. **Answer:** $5 \frac{\text{yd}}{\text{min}} = 900 \frac{\text{ft}}{\text{hr}}$. 6. **Determine if the stone is real gold by comparing densities.** 7. Given: - Mass $m = 325 \text{ g}$ - Diameter $d = 5 \text{ cm}$ - Radius $r = \frac{d}{2} = 2.5 \text{ cm}$ - Density of gold $\rho_{gold} = 19.3 \frac{\text{g}}{\text{cm}^3}$ 8. Calculate the volume of the sphere using: $$V = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (2.5)^3 = \frac{4}{3} \pi 15.625 = 65.45 \text{ cm}^3$$ 9. Calculate the density of the stone: $$\rho = \frac{m}{V} = \frac{325}{65.45} = 4.96 \frac{\text{g}}{\text{cm}^3}$$ 10. Compare the stone's density to gold's density: $$4.96 \frac{\text{g}}{\text{cm}^3} \neq 19.3 \frac{\text{g}}{\text{cm}^3}$$ 11. Since the stone's density is much less than gold's, it is unlikely to be real gold. **Final answers:** - $5 \frac{\text{yd}}{\text{min}} = 900 \frac{\text{ft}}{\text{hr}}$ - The stone is not real gold based on density comparison.