5.4 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?

To determine how long it will take John to catch up with Karabo, we first need to find out how far Karabo has traveled by the time John starts driving. Since he started an hour earlier at a speed of \(80 \mathrm{~km/h}\), he has traveled: \[ \text{Distance (Karabo)} = \text{Speed} \times \text{Time} = 80 \mathrm{~km/h} \times 1 \mathrm{~h} = 80 \mathrm{~km} \] Now, let's denote the time it takes for John to catch up with Karabo as \(t\) hours after John has started driving. During this time, John will cover a distance equal to: \[ \text{Distance (John)} = 100 \mathrm{~km/h} \times t \] In that same amount of time \(t\), Karabo will continue driving and cover additional distance: \[ \text{Distance (Karabo, after John's start)} = 80 \mathrm{~km/h} \times t \] To find out when John catches up to Karabo, we set the total distance traveled by John equal to the distance Karabo traveled plus the initial distance he had: \[ 100t = 80 + 80t \] Now, solve for \(t\): \[ 100t - 80t = 80 \] \[ 20t = 80 \] \[ t = \frac{80}{20} = 4 \] Therefore, it will take John 4 hours to catch up with Karabo.