EXERCISE 7 You may use a calculator in this exercise. Assume that the rates remain constant. (a) What is the speed, in $$ \mathrm{km} / \mathrm{h} $$, of a car that travels a distance of 240 km in 3 hours? (b) The temperature in a room changed from $$ 9^{\circ} \mathrm{C} $$ to $$ 27^{\circ} \mathrm{C} $$ in 3 minutes. What is the rate change of temperature in $$ { }^{\circ} \mathrm{C} / \mathrm{min} $$ ? (c) If $$ 50 l $$ of liquid has a mass of 100 kg , what is the density of the liquid in $$ \mathrm{g} / \mathrm{cm} $$

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Let's solve each part of Exercise 7 step by step.

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### **Part (a)**

**Question:**
What is the speed, in $$ \mathrm{km} / \mathrm{h} $$, of a car that travels a distance of 240 km in 3 hours?

**Solution:**
Speed is calculated using the formula:
$$
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
$$

Given:
- Distance = 240 km
- Time = 3 hours

$$
\text{Speed} = \frac{240 \, \text{km}}{3 \, \text{h}} = 80 \, \mathrm{km/h}
$$

**Answer:**  
The speed of the car is **80  km/h**.

---

### **Part (b)**

**Question:**
The temperature in a room changed from $$ 9^{\circ} \mathrm{C} $$ to $$ 27^{\circ} \mathrm{C} $$ in 3 minutes. What is the rate change of temperature in $$ {}^{\circ} \mathrm{C} / \mathrm{min} $$?

**Solution:**
The rate of temperature change is calculated using the formula:
$$
\text{Rate of Change} = \frac{\Delta T}{\Delta t}
$$
where:
- $$ \Delta T $$ is the change in temperature
- $$ \Delta t $$ is the change in time

Given:
- Initial Temperature ($$ T_i $$) = $$ 9^{\circ} \mathrm{C} $$
- Final Temperature ($$ T_f $$) = $$ 27^{\circ} \mathrm{C} $$
- Time ($$ \Delta t $$) = 3 minutes

Calculate $$ \Delta T $$:
$$
\Delta T = T_f - T_i = 27^{\circ} \mathrm{C} - 9^{\circ} \mathrm{C} = 18^{\circ} \mathrm{C}
$$

Now, calculate the rate:
$$
\text{Rate of Change} = \frac{18^{\circ} \mathrm{C}}{3 \, \text{min}} = 6^{\circ} \mathrm{C}/\text{min}
$$

**Answer:**  
The rate of temperature change is **6 °C/min**.

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### **Part (c)**

**Question:**
If $$ 50 \, \text{l} $$ of liquid has a mass of 100 kg, what is the density of the liquid in $$ \mathrm{g}/\mathrm{cm}^3 $$?

**Solution:**
Density is calculated using the formula:
$$
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
$$

First, convert the given units to $$ \mathrm{g} $$ and $$ \mathrm{cm}^3 $$:
- Mass: $$ 100 \, \text{kg} = 100,000 \, \text{g} $$ (since $$ 1 \, \text{kg} = 1,000 \, \text{g} $$)
- Volume: $$ 50 \, \text{l} = 50,000 \, \text{cm}^3 $$ (since $$ 1 \, \text{l} = 1,000 \, \text{cm}^3 $$)

Now, calculate the density:
$$
\text{Density} = \frac{100,000 \, \text{g}}{50,000 \, \text{cm}^3} = 2 \, \mathrm{g}/\mathrm{cm}^3
$$

**Answer:**  
The density of the liquid is **2 g/cm³**.

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**Part (a):** The car's speed is **80 km/h**. **Part (b):** The temperature changed at a rate of **6 °C/min**. **Part (c):** The liquid's density is **2 g/cm³**.

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