(b) The temperature in a room changed from \( 9^{\circ} \mathrm{C} \) to \( 27^{\circ} \mathrm{C} \) in 3 minutes. What is the rate of change of temperature in \( { }^{\circ} \mathrm{C} / \mathrm{min} \) ? If \( 50 / \) of liquid has a mass of 100 kg , what is the density of the liquid in \( \mathrm{g} / \mathrm{cm}^{3} \) ? Note: \( 1 /=1000 \mathrm{~cm}^{3} \) (d) If Aidan runs 10 km in 25 minutes, what is his speed in \( \mathrm{km} / \mathrm{h} \) ? (e) A container is filled, from empty, with water, at a rate of \( 30 \mathrm{l} / \mathrm{min} \). (1) How much water will be in the container after an hour? (2) If the container has a capacity of \( 6 \mathrm{k} / \), how long does it take to fill the container up

Certainly! Let's address each part of your problem set step by step. --- ### (b) Rate of Change of Temperature **Given:** - Initial Temperature, \( T_{\text{initial}} = 9^{\circ} \mathrm{C} \) - Final Temperature, \( T_{\text{final}} = 27^{\circ} \mathrm{C} \) - Time taken, \( \Delta t = 3 \) minutes **Solution:** The rate of change of temperature is calculated using the formula: \[ \text{Rate} = \frac{\Delta T}{\Delta t} \] where \( \Delta T = T_{\text{final}} - T_{\text{initial}} \). \[ \Delta T = 27^{\circ} \mathrm{C} - 9^{\circ} \mathrm{C} = 18^{\circ} \mathrm{C} \] \[ \text{Rate} = \frac{18^{\circ} \mathrm{C}}{3 \, \text{min}} = 6^{\circ} \mathrm{C}/\text{min} \] **Answer:** The rate of change of temperature is **6 °C/min**. --- ### (c) Density of the Liquid **Given:** - Volume of liquid, \( V = 50 \) liters - Mass of liquid, \( m = 100 \) kg - Note: \( 1\, \text{L} = 1000\, \text{cm}^3 \) **Solution:** First, convert the mass to grams and volume to cubic centimeters to find density in \( \mathrm{g}/\mathrm{cm}^3 \). \[ m = 100\, \text{kg} = 100,000\, \text{g} \] \[ V = 50\, \text{L} = 50 \times 1000\, \text{cm}^3 = 50,000\, \text{cm}^3 \] \[ \text{Density}, \rho = \frac{m}{V} = \frac{100,000\, \text{g}}{50,000\, \text{cm}^3} = 2\, \mathrm{g}/\mathrm{cm}^3 \] **Answer:** The density of the liquid is **2 g/cm³**. --- ### (d) Aidan's Running Speed in km/h **Given:** - Distance run, \( d = 10 \) km - Time taken, \( t = 25 \) minutes **Solution:** First, convert time from minutes to hours. \[ t = 25\, \text{minutes} = \frac{25}{60}\, \text{hours} = \frac{5}{12}\, \text{hours} \] \[ \text{Speed}, v = \frac{d}{t} = \frac{10\, \text{km}}{\frac{5}{12}\, \text{hours}} = 10 \times \frac{12}{5} = 24\, \text{km/h} \] **Answer:** Aidan's speed is **24 km/h**. --- ### (e) Water Filling the Container **Given:** - Filling rate, \( R = 30\, \text{L/min} \) #### (1) Amount of Water After One Hour **Solution:** First, convert time to minutes. \[ \text{Time}, t = 1\, \text{hour} = 60\, \text{minutes} \] \[ \text{Volume filled}, V = R \times t = 30\, \text{L/min} \times 60\, \text{min} = 1800\, \text{L} \] **Answer:** After one hour, **1800 liters** of water will be in the container. #### (2) Time to Fill a 6 kL Container **Given:** - Container capacity, \( C = 6\, \text{kL} = 6000\, \text{L} \) **Solution:** \[ \text{Time}, t = \frac{C}{R} = \frac{6000\, \text{L}}{30\, \text{L/min}} = 200\, \text{minutes} \] Convert minutes to hours and minutes if desired. \[ 200\, \text{minutes} = 3\, \text{hours} \, 20\, \text{minutes} \] **Answer:** It takes **200 minutes** (or **3 hours and 20 minutes**) to fill the 6 kL container. --- If you have any further questions or need additional explanations, feel free to ask!