Question: User: A submarine falls 200m for each 40m across and a torpedo falls 420m for each 80m across in pursuit of the submarine. Which has the steeper gradient, the submarine or torpedo?
1. **State the problem:** We need to find which has the steeper gradient: the submarine or the torpedo.
2. **Formula for gradient:** Gradient (slope) is calculated as the ratio of vertical change to horizontal change, i.e., $$\text{gradient} = \frac{\text{vertical change}}{\text{horizontal change}}$$.
3. **Calculate submarine gradient:**
$$\text{submarine gradient} = \frac{200}{40}$$
Simplify:
$$= \frac{\cancel{200}}{\cancel{40}} = 5$$
4. **Calculate torpedo gradient:**
$$\text{torpedo gradient} = \frac{420}{80}$$
Simplify:
$$= \frac{\cancel{420}}{\cancel{80}} = \frac{21}{4} = 5.25$$
5. **Compare gradients:**
Submarine gradient = $5$
Torpedo gradient = $5.25$
6. **Conclusion:** Since $5.25 > 5$, the torpedo has the steeper gradient than the submarine.