Karabo and John are at the same rest stop alongside a highway. Karabo started omng airng the highway at a constant speed of \( 80 \mathrm{~km} / \mathrm{m} \). An hour later, John sterfed drving along the same highway in the same direction as Karabo at the constant speed of \( 100 \mathrm{~km} / \mathrm{h} \). How long will it take John to catch up with Karabo?

To find out how long it will take John to catch up with Karabo, we first need to determine how far Karabo has traveled when John starts. Since Karabo has a one-hour head start at a speed of \( 80 \, \mathrm{km/h} \), he will have traveled \( 80 \, \mathrm{km} \). Now, we can set up an equation. Let \( t \) be the time in hours that John drives until he catches up. In that time, John travels \( 100t \) kilometers, and Karabo, who has been driving for \( t + 1 \) hours, travels \( 80(t + 1) \) kilometers. We want to set these distances equal to one another since this is the point where John catches up with Karabo: \[ 100t = 80(t + 1) \] Expanding the right side gives: \[ 100t = 80t + 80 \] Now, solving for \( t \): \[ 100t - 80t = 80 \] \[ 20t = 80 \] \[ t = 4 \] Therefore, it will take John 4 hours to catch up with Karabo! Now, let’s add some extra information to keep things fun. John’s speed of \( 100 \, \mathrm{km/h} \) might seem fast, but it's actually quite common for highway driving in various countries. The exhilarating feeling of cruising along at such speeds is a thrill for many, especially in sporty cars designed for performance! On the other hand, next time you venture out on a long road trip, remember that smart planning can prevent a race like this! Making use of apps for real-time traffic updates can help you avoid backlogs, ensuring a smooth drive without the need for speed!