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 ra change of temperature in \( { }^{\circ} \mathrm{C} / \mathrm{min} \) ? (c) If \( 50 ~ \) of liquid has a mass of 100 kg , what is the density of the liquid in \( \mathrm{g} / \) Note: \( 1 l=1000 \mathrm{~cm}^{3} \) (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 kl , how long does it take to fill the contail

Sure, let's solve each part of **EXERCISE 7** step by step. --- ### **(a) Calculating the Speed of the Car** **Problem:** What is the speed, in \( \text{km/h} \), of a car that travels a distance of **240 km** in **3 hours**? **Solution:** The formula to calculate speed is: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] Plugging in the given values: \[ \text{Speed} = \frac{240 \, \text{km}}{3 \, \text{h}} = 80 \, \text{km/h} \] **Answer:** The car's speed is **80 km/h**. --- ### **(b) Determining the Rate of Temperature Change** **Problem:** The temperature in a room changed from \( 9^\circ \text{C} \) to \( 27^\circ \text{C} \) in **3 minutes**. What is the rate of change of temperature in \( \frac{^\circ \text{C}}{\text{min}} \)? **Solution:** First, calculate the change in temperature: \[ \Delta T = 27^\circ \text{C} - 9^\circ \text{C} = 18^\circ \text{C} \] Next, calculate the rate of change: \[ \text{Rate} = \frac{\Delta T}{\Delta t} = \frac{18^\circ \text{C}}{3 \, \text{min}} = 6^\circ \text{C/min} \] **Answer:** The temperature increases at a rate of **6 °C per minute**. --- ### **(c) Finding the Density of the Liquid** **Problem:** If **50 liters** of liquid have a mass of **100 kg**, what is the density of the liquid in \( \frac{\text{g}}{\text{cm}^3} \)? **Solution:** **Step 1: Convert Mass to Grams** \[ 100 \, \text{kg} = 100 \times 1000 \, \text{g} = 100{,}000 \, \text{g} \] **Step 2: Convert Volume to Cubic Centimeters** \[ 1 \, \text{liter} = 1000 \, \text{cm}^3 \\ 50 \, \text{liters} = 50 \times 1000 \, \text{cm}^3 = 50{,}000 \, \text{cm}^3 \] **Step 3: Calculate Density** \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{100{,}000 \, \text{g}}{50{,}000 \, \text{cm}^3} = 2 \, \frac{\text{g}}{\text{cm}^3} \] **Answer:** The density of the liquid is **2 g/cm³**. --- ### **(d) Calculating Aidan's Running Speed** **Problem:** If Aidan runs **10 km** in **25 minutes**, what is his speed in \( \text{km/h} \)? **Solution:** First, convert time from minutes to hours: \[ 25 \, \text{minutes} = \frac{25}{60} \, \text{hours} \approx 0.4167 \, \text{hours} \] Then, use the speed formula: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{10 \, \text{km}}{0.4167 \, \text{h}} \approx 24 \, \text{km/h} \] **Answer:** Aidan's speed is approximately **24 km/h**. --- ### **(e) Analyzing the Water Filling the Container** **Problem:** A container is filled, from empty, with water at a rate of **30 liters per minute**. 1. **How much water will be in the container after an hour?** 2. **If the container has a capacity of 6 kiloliters (kl), how long does it take to fill the container?** --- #### **(e)(1) Calculating Water After One Hour** **Solution:** First, convert one hour to minutes: \[ 1 \, \text{hour} = 60 \, \text{minutes} \] Then, calculate the total volume: \[ \text{Volume} = \text{Rate} \times \text{Time} = 30 \, \frac{\text{liters}}{\text{min}} \times 60 \, \text{min} = 1800 \, \text{liters} \] **Answer:** After one hour, the container will have **1,800 liters** of water. --- #### **(e)(2) Determining Time to Fill a 6 kiloliter Container** **Solution:** First, understand the capacity in liters: \[ 6 \, \text{kl} = 6 \times 1000 \, \text{liters} = 6000 \, \text{liters} \] Then, calculate the time required: \[ \text{Time} = \frac{\text{Volume}}{\text{Rate}} = \frac{6000 \, \text{liters}}{30 \, \frac{\text{liters}}{\text{min}}} = 200 \, \text{minutes} \] Convert minutes to hours and minutes: \[ 200 \, \text{minutes} = 3 \, \text{hours} \, 20 \, \text{minutes} \] **Answer:** It takes **200 minutes** (which is **3 hours and 20 minutes**) to fill the container. ---