CLASSwORte You may use a calculator in this exercise. Assurfe that the rates remt (a) A car travels at \( 80 \mathrm{~km} / \mathrm{h} \). (1) How long does it take to travel 320 km ? (2) How far will the car travel in 10 hours? (3) Convert this rate \( (80 \mathrm{~km} / \mathrm{h}) \) to a rate measured in \( \mathrm{m} / \mathrm{s} \), (b) If you can consistently run 80 m in 16 s , (1) how long will it take you to run 400 m ? (2) how far can you run in I minute and 4 seconds? c) A car consumes fuel at a rate of \( 8 / / 100 \mathrm{~km} \). (1) How many litres is needed to travel 400 km ? (2) How far you can travel with 50 l ?

Let's break down the problem step by step, addressing each part systematically. ### Part (a) 1. **How long does it take to travel 320 km?** - We can use the formula for time, which is: \[ t = \frac{d}{r} \] where \( d \) is distance and \( r \) is rate. - Here, \( d = 320 \) km and \( r = 80 \) km/h. - Plugging in the values: \[ t = \frac{320 \text{ km}}{80 \text{ km/h}} = 4 \text{ hours} \] 2. **How far will the car travel in 10 hours?** - We can use the formula for distance, which is: \[ d = r \times t \] - Here, \( r = 80 \) km/h and \( t = 10 \) hours. - Plugging in the values: \[ d = 80 \text{ km/h} \times 10 \text{ h} = 800 \text{ km} \] 3. **Convert this rate \( (80 \text{ km/h}) \) to a rate measured in \( \text{m/s} \).** - To convert km/h to m/s, we use the conversion factor \( \frac{1000 \text{ m}}{1 \text{ km}} \) and \( \frac{1 \text{ h}}{3600 \text{ s}} \): \[ r = 80 \text{ km/h} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ h}}{3600 \text{ s}} = \frac{80000 \text{ m}}{3600 \text{ s}} \approx 22.22 \text{ m/s} \] ### Part (b) 1. **How long will it take you to run 400 m?** - First, we need to find the running rate: \[ r = \frac{80 \text{ m}}{16 \text{ s}} = 5 \text{ m/s} \] - Now, using the time formula: \[ t = \frac{d}{r} = \frac{400 \text{ m}}{5 \text{ m/s}} = 80 \text{ seconds} \] 2. **How far can you run in 1 minute and 4 seconds?** - First, convert 1 minute and 4 seconds to seconds: \[ 1 \text{ minute} = 60 \text{ seconds} \quad \Rightarrow \quad 1 \text{ minute and 4 seconds} = 60 + 4 = 64 \text{ seconds} \] - Now, using the distance formula: \[ d = r \times t = 5 \text{ m/s} \times 64 \text{ s} = 320 \text{ m} \] ### Part (c) 1. **How many litres are needed to travel 400 km?** - The fuel consumption rate is \( 8 \text{ L} / 100 \text{ km} \). - To find the litres needed for 400 km: \[ \text{Litres} = \frac{8 \text{ L}}{100 \text{ km}} \times 400 \text{ km} = 32 \text{ L} \] 2. **How far can you travel with 50 L?** - Using the same fuel consumption rate: \[ \text{Distance} = \frac{100 \text{ km}}{8 \text{ L}} \times 50 \text{ L} = 625 \text{ km} \] ### Summary of Answers - (a)(1) 4 hours - (a)(2) 800 km - (a)(3) 22.22 m/s - (b)(1) 80 seconds - (b)(2) 320 m - (c)(1) 32 L - (c)(2) 625 km