To find when the car catches up with the bus, we need to determine how far ahead the bus is when the car starts and then calculate the time it takes for the car to cover that distance.

Step 1: Calculate the head start of the bus

The bus leaves at 7:30 AM and the car leaves at 9:30 AM, meaning the bus has a 2-hour head start.

• In 2 hours, the bus travels: $\text{Distance} = \text{Speed} \times \text{Time} = 60 \, \text{km/h} \times 2 \, \text{h} = 120 \, \text{km}$ So, the bus is 120 km ahead when the car starts.

Step 2: Determine the relative speed

The car travels faster than the bus. The difference in their speeds is: $\text{Relative speed} = 100 \, \text{km/h} - 60 \, \text{km/h} = 40 \, \text{km/h}$

Step 3: Calculate the time for the car to catch up

Now, we use the relative speed to find how long it takes the car to cover the 120 km head start: $\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{120 \, \text{km}}{40 \, \text{km/h}} = 3 \, \text{hours}$

Step 4: Find the time of the day when the car catches up

The car starts at 9:30 AM and takes 3 hours to catch up. Therefore, the car catches up with the bus at: $9:30 \, \text{AM} + 3 \, \text{hours} = 12:30 \, \text{PM}$

Final Answer:

The car catches up with the bus at 12:30 PM.

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Would you like further details or have any questions?

Here are 8 related questions to expand your understanding:

1. What if the car started at 8:30 AM instead of 9:30 AM?
2. How would the problem change if the bus traveled at 80 km/h instead of 60 km/h?
3. What is the distance traveled by the car when it catches up with the bus?
4. How long would it take for the car to catch up if it traveled at 90 km/h instead of 100 km/h?
5. What is the distance between the bus and the car after 1 hour if the car starts at 9:30 AM?
6. How would you calculate the point where they meet on a map?
7. How does the difference in speed affect the time of catching up?
8. What if both vehicles had started at the same time but with their respective speeds?

Tip: When solving problems involving relative speed, always focus on the difference in speed when calculating the time it takes to close the gap.