# Step-by-Step Solution ## 1. **Convert Rocket Speed to m/s** Given: - Rocket speed = \( 28323.1 \) km/hr Convert km/hr to m/s: \[ 1 \text{ km} = 100 \text{ m} \] \[ 1 \text{ hr} = 360 \text{ s} \] \[ \text{Speed in m/s} = 28323.1 \times \frac{100}{360} \] \[ \text{Speed in m/s} = 28323.1 \times .27778 \approx 7874.2\ \text{m/s} \] --- ## 2. **Given Speed of Sound** \[ \text{Speed of sound} = 340\ \text{m/s} \] --- ## 3. **Find How Many Times Faster** \[ \text{Ratio} = \frac{\text{Rocket speed}}{\text{Speed of sound}} \] \[ \text{Ratio} = \frac{7874.2}{340} \] \[ \text{Ratio} \approx 23.16 \] --- ## 4. **Final Answer** The rocket is **23.1 times faster** than the speed of sound. (Rounded to 3 significant figures, matching the options.) ### **Matching Option** - **8.33 times faster** - **8.33 x 10^3 times faster** - **2.31 x 10^2 times faster** - **2.31 times faster** - **1.13 x 10^6 times faster** The correct answer is: \[ \boxed{2.31 \times 10^{1} \text{ times faster}} \] But among the provided options, **none is exactly 23.1**, but **2.31 x 10^1** (i.e., 23.1) is equivalent to **2.31 x 10^1**. **Closest among the options:** - **2.31 x 10^1 times faster** (if allowed) - If you must pick from the available options, **2.31 x 10^2 = 231** is closest in format, but not value. - **23.1** matches **2.31 x 10^1** **If "2.31 x 10^2" is the only scientific notation option, but 23.1 is not an option, the answer provided in the list does not match the actual solution.** ## **Summary Table** | Calculation | Value | |------------------------|-------------| | Rocket speed (m/s) | 7874.2 | | Speed of sound (m/s) | 340 | | Ratio | 23.1 | --- ## **Final Answer** > **The rocket is 23.1 times faster than the speed of sound. The correct answer is \( 2.31 \times 10^1 \) times faster (if available).** > > If only the options given above are allowed, none exactly matches the correct value, but **2.31 x 10^1 times faster** would be the answer if present.