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\begin{tabular}{l} Karabo and John are at the same rest stop alongside a highway. Karabo \\ started driving along the highway at a constant speed of \( 80 \mathrm{~km} / \mathrm{h} \). An hour \\ later, John started driving 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? \\ \hline\end{tabular}

Ask by Fowler Gonzalez. in South Africa
Mar 09,2025

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John will catch up with Karabo after 4 hours.

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To catch up with Karabo, John needs to close the gap created by Karabo's head start. Since Karabo starts driving an hour earlier at 80 km/h, he will have covered a distance of: \[ \text{Distance} = \text{Speed} \times \text{Time} = 80 \, \text{km/h} \times 1 \, \text{h} = 80 \, \text{km} \] Now, the relative speed between John and Karabo is: \[ \text{Relative Speed} = \text{John's Speed} - \text{Karabo's Speed} = 100 \, \text{km/h} - 80 \, \text{km/h} = 20 \, \text{km/h} \] To find out how long it will take for John to catch up with Karabo, we use the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{80 \, \text{km}}{20 \, \text{km/h}} = 4 \, \text{h} \] So, it will take John 4 hours to catch up with Karabo!

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