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 \( \mathrm{g} / \mathrm{cm} \)

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