Pregunta
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Kearabo and John are of the same rest stop alongside a highuoy. harobo sharted drivirg olong the high way at a constant speed \( 80 \mathrm{~km} / \mathrm{h} \). An heur laher; John started driving along the same high way in the sme direction as Karibo at a constant speed of 100 km h. How long will it take Jolin to catch up with Kanabo?

Ask by Dawson Mills. in South Africa
Mar 12,2025

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John will catch up with Karibo 4 hours after he starts driving.

Solución

1. Let \( t \) denote the time (in hours) that John drives until he catches up with Karibo. 2. Karibo starts driving one hour before John. Therefore, by the time John starts, Karibo has already traveled a distance of \[ 80 \times 1 = 80 \text{ km}. \] 3. Once John starts driving, Karibo and John travel at constant speeds of \(80 \, \text{km/h}\) and \(100 \, \text{km/h}\) respectively. 4. In time \( t \), Karibo covers an additional distance of \[ 80t \text{ km}, \] while John covers \[ 100t \text{ km}. \] 5. Since John catches up with Karibo when they have traveled the same total distance from the rest stop, we equate: \[ 80 + 80t = 100t. \] 6. Solving for \( t \): \[ 80 = 100t - 80t \quad \Longrightarrow \quad 80 = 20t, \] \[ t = \frac{80}{20} = 4 \text{ hours}. \] John will catch up with Karibo 4 hours after he starts driving.

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Bonus Knowledge

To figure out how long it will take John to catch up with Kearabo, we can start by determining the head start that Kearabo has. Kearabo drives for 1 hour at 80 km/h, so by the time John starts, Kearabo is already 80 km ahead. Since John is driving faster at 100 km/h, we can calculate the rate at which he closes the gap. The difference in their speeds is \(100 \text{ km/h} - 80 \text{ km/h} = 20 \text{ km/h}\). Now, to find out how long it takes for John to close an 80 km gap at 20 km/h, we can use the formula: Time = Distance / Speed. So, Time = \(80 \text{ km} / 20 \text{ km/h} = 4 \text{ hours}\). Therefore, it will take John 4 hours to catch up with Kearabo! John's drive showcases how timing and speed can lead to winning the race! Imagine them both cruising down the highway; while Kearabo’s scenic drive seems calm, John's determination and speed create quite the adventure. It’s like watching a thrilling chase scene where the suspense builds up until John finally closes the distance. To keep your math skills sharp when dealing with similar problems, remember the key concepts of relative speed and time management. Instead of just plugging numbers in, visualize the situation: picture their journey, perhaps with Kearabo driving leisurely while John rockets ahead! And don't forget: double-check your calculations, as it’s easy to mix up distance, speed, and time. Keeping those elements in sync will help avoid mistakes!

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