Question: 2. Maria is monitoring the temperature of two substances in her science lab. Substance A is currently $96.2$° and rising $1.5$° each minute. Substance B is currently $98.5$° and cooling $0.8$° each minute. After how many minutes will the two substances be at the same temperature?
a. Equation: __________
b. Solution __________
1. **State the problem:** We want to find after how many minutes the temperatures of Substance A and Substance B will be equal.
2. **Define variables:** Let $t$ be the number of minutes after which the temperatures are the same.
3. **Write expressions for temperatures:**
- Temperature of Substance A after $t$ minutes: $$96.2 + 1.5t$$
- Temperature of Substance B after $t$ minutes: $$98.5 - 0.8t$$
4. **Set up the equation:** Since the temperatures are equal at time $t$, we have
$$96.2 + 1.5t = 98.5 - 0.8t$$
5. **Solve the equation:**
Add $0.8t$ to both sides:
$$96.2 + 1.5t + 0.8t = 98.5 - 0.8t + 0.8t$$
$$96.2 + 2.3t = 98.5$$
Subtract $96.2$ from both sides:
$$96.2 - 96.2 + 2.3t = 98.5 - 96.2$$
$$2.3t = 2.3$$
Divide both sides by $2.3$:
$$\frac{\cancel{2.3}t}{\cancel{2.3}} = \frac{2.3}{2.3}$$
$$t = 1$$
6. **Interpretation:** After $1$ minute, the temperatures of Substance A and Substance B will be the same.
**Final answer:** $t = 1$ minute.