\( 4 \begin{array}{l}100 \mathrm{ml} \text { of sugar weighs } 80 \mathrm{~g} \text { - } \\ 4.1 \text { What weight of sugar will be required for a recipe tha } \\ \text { needs } 2500 \mathrm{ml} \text { of sugar? } \\ 4.2 \text { A recipe asks for } 1,5 \mathrm{~kg} \text { of sugar. How many ml of sugs } \\ \text { is needed? }\end{array} \) 5 Determine how long it will take for a vehicle travelling ata speed of \( 105 \mathrm{~km} / \mathrm{h} \) to travel a distance of 75 km .

Sure, let's address each of your questions step by step. --- ### **4. Sugar Conversion Problems** **Given:** - **Density of Sugar**: \(100 \text{ ml} = 80 \text{ g}\) This implies: \[ \text{Density} = \frac{80 \text{ g}}{100 \text{ ml}} = 0.8 \text{ g/ml} \] #### **4.1. Weight of Sugar Required for 2500 ml** **Problem:** What weight of sugar is required for a recipe that needs **2500 ml** of sugar? **Solution:** Use the density to find the weight. \[ \text{Weight} = \text{Density} \times \text{Volume} = 0.8 \text{ g/ml} \times 2500 \text{ ml} = 2000 \text{ g} \] **Convert grams to kilograms (if needed):** \[ 2000 \text{ g} = 2 \text{ kg} \] **Answer:** **2000 grams (2 kilograms)** of sugar are required. #### **4.2. Volume of Sugar Needed for 1.5 kg** **Problem:** A recipe asks for **1.5 kg** of sugar. How many ml of sugar is needed? **Solution:** First, convert kilograms to grams: \[ 1.5 \text{ kg} = 1500 \text{ g} \] Now, use the density to find the volume: \[ \text{Volume} = \frac{\text{Weight}}{\text{Density}} = \frac{1500 \text{ g}}{0.8 \text{ g/ml}} = 1875 \text{ ml} \] **Answer:** **1875 milliliters** of sugar are needed. --- ### **5. Time Required for a Vehicle to Travel 75 km at 105 km/h** **Given:** - **Speed**: \(105 \text{ km/h}\) - **Distance**: \(75 \text{ km}\) **Problem:** Determine how long it will take for a vehicle traveling at a speed of **105 km/h** to travel a distance of **75 km**. **Solution:** Use the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{75 \text{ km}}{105 \text{ km/h}} \] Simplify the fraction: \[ \text{Time} = \frac{75}{105} \text{ hours} = \frac{5}{7} \text{ hours} \approx 0.7143 \text{ hours} \] Convert hours to minutes: \[ 0.7143 \text{ hours} \times 60 \text{ minutes/hour} \approx 42.86 \text{ minutes} \] **Answer:** It will take approximately **42.9 minutes** for the vehicle to travel 75 km at a speed of 105 km/h. --- If you have any further questions or need additional assistance, feel free to ask!