Question: 2) Chelsea left the hardware store and drove toward her cabin on the lake at an average speed of $70$ km/h. Stephanie left four hours later and drove in the opposite direction with an average speed of $65$ km/h. Find the number of hours Stephanie needs to drive before they are $415$ km apart.
1. **State the problem:**
Chelsea drives away from the hardware store at $70$ km/h. Stephanie starts $4$ hours later, driving in the opposite direction at $65$ km/h. We want to find how many hours Stephanie drives before the distance between them is $415$ km.
2. **Define variables:**
Let $t$ be the number of hours Stephanie drives.
3. **Express distances:**
Chelsea's driving time when Stephanie has driven $t$ hours is $t + 4$ hours.
Chelsea's distance: $$70(t + 4)$$
Stephanie's distance: $$65t$$
4. **Since they drive in opposite directions, their distances add up to the total distance apart:**
$$70(t + 4) + 65t = 415$$
5. **Simplify the equation:**
$$70t + 280 + 65t = 415$$
$$135t + 280 = 415$$
6. **Isolate $t$:**
$$135t = 415 - 280$$
$$135t = 135$$
7. **Divide both sides by 135:**
$$t = \frac{135}{135}$$
$$t = 1$$
8. **Interpretation:**
Stephanie needs to drive for $1$ hour before they are $415$ km apart.
**Final answer:** $1$ hour (Option B).