We can solve this problem by determining when Car B will catch up to Car A. Let's break it down step by step:

Step 1: Calculate the head start of Car A

Car A leaves at 11:00 a.m., and Car B leaves at 1:00 p.m. Therefore, Car A has a head start of 2 hours before Car B starts.

During these 2 hours, Car A is traveling at an average speed of 70 km/h, so the distance Car A travels in those 2 hours is: $\text{Distance} = \text{Speed} \times \text{Time} = 70 \, \text{km/h} \times 2 \, \text{hours} = 140 \, \text{km}.$

Step 2: Determine the relative speed

Car B is traveling faster than Car A. The relative speed at which Car B is closing the gap on Car A is: $\text{Relative Speed} = \text{Speed of Car B} - \text{Speed of Car A} = 90 \, \text{km/h} - 70 \, \text{km/h} = 20 \, \text{km/h}.$

Step 3: Calculate the time taken for Car B to catch up

To catch Car A, Car B needs to close the 140 km gap. The time it takes to do so is given by: $\text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{140 \, \text{km}}{20 \, \text{km/h}} = 7 \, \text{hours}.$

Step 4: Determine the time when Car B catches up

Since Car B left at 1:00 p.m., we add the 7 hours to this time: $1:00 \, \text{p.m.} + 7 \, \text{hours} = 8:00 \, \text{p.m.}.$

Conclusion:

Car B will catch Car A at 8:00 p.m..

Would you like more details or have any questions about the solution?

Here are 5 related questions for further exploration:

1. How far will Car A and Car B have traveled when Car B catches up?
2. If Car B had started at 12:00 p.m. instead, when would it catch Car A?
3. What is the total distance from Melbourne to Adelaide if Car B reaches Adelaide by 10:00 p.m.?
4. How much time would it take for Car A to reach Adelaide at a constant speed of 70 km/h?
5. If Car A increased its speed to 80 km/h, how would the catch-up time change?

Tip: When solving catch-up problems, always identify the head start and calculate the relative speed to find the time needed for one object to catch the other.