much earlier would it have arrived at B? Two men running towards each other at \( 4 \mathrm{~m} / \mathrm{s} \) and \( 6 \mathrm{~m} / \mathrm{s} \), respectively, are one kilometre apart. How long will it tak before they meet?

To determine how long it takes for the two men to meet, you can use the concept of **relative speed**. Here's a step-by-step breakdown: 1. **Given:** - **Speed of the first man (\( v_1 \))**: 4 m/s - **Speed of the second man (\( v_2 \))**: 6 m/s - **Initial distance between them (\( d \))**: 1 kilometer = 1000 meters 2. **Relative Speed (\( v_{\text{relative}} \)):** When two objects are moving towards each other, their relative speed is the sum of their individual speeds. \[ v_{\text{relative}} = v_1 + v_2 = 4\, \text{m/s} + 6\, \text{m/s} = 10\, \text{m/s} \] 3. **Time to Meet (\( t \)):** Time is calculated by dividing the initial distance by the relative speed. \[ t = \frac{d}{v_{\text{relative}}} = \frac{1000\, \text{meters}}{10\, \text{m/s}} = 100\, \text{seconds} \] 4. **Conclusion:** The two men will meet after **100 seconds**. --- **Additional Perspective:** - **Converting Seconds to Minutes:** If you prefer to see the time in minutes: \[ 100\, \text{seconds} = \frac{100}{60} \approx 1.67\, \text{minutes} \] So, they will meet approximately **1 minute and 40 seconds** after they start running towards each other. - **Visual Representation:** - Imagine both men starting 1 kilometer apart. - Every second, together, they cover 10 meters (since 4 m/s + 6 m/s = 10 m/s). - In 100 seconds, they would have covered the entire distance between them. If you have any further questions or need clarification on any step, feel free to ask!