The problem you're dealing with is a relative velocity problem. Here's the key information from the image:

• One car is traveling at 60 km/h (the slower car).
• The other car is traveling at 80 km/h (the faster car).
• The slower car is 110 km ahead of the faster car.
• The question asks: If it is now 3:30 PM, and the cars continue to travel at the same rates, when will the faster car catch up to the slower car?

Steps to solve:

1. Relative velocity:

   • The relative velocity of the faster car compared to the slower car is: $80 \, \text{km/h} - 60 \, \text{km/h} = 20 \, \text{km/h}$

2. Time to catch up:

   • The faster car needs to cover a distance of 110 km at the relative speed of 20 km/h.
   • Using the formula for time: $\text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{110 \, \text{km}}{20 \, \text{km/h}} = 5 \, \text{hours}$

3. Final time:

   • If it is currently 3:30 PM, then adding 5 hours will give the time the faster car catches up.
   • 3:30 PM + 5 hours = 8:30 PM.

Answer:

The faster car will catch up to the slower car at 8:30 PM.

Would you like further details or clarifications?

Here are five related questions:

1. How would the solution change if both cars increased their speed equally?
2. What if the slower car was initially 150 km ahead?
3. How would the answer change if the faster car could accelerate over time?
4. Can you express this problem as a system of equations?
5. How can you use a graph to visually show the moment they meet?

Tip: Relative velocity is crucial when analyzing the movement of two objects in the same direction or opposing directions.