To solve this problem, we need to calculate the distance between location P (starting point) and location Q (the point where 'B' meets 'A').

Step 1: Understand the time difference

• 'A' starts at 1:00 p.m. with a speed of 1 m/s.
• 'B' starts at 1:10 p.m., 10 minutes later, with a speed of 2 m/s.

In those 10 minutes (600 seconds), 'A' travels at 1 m/s: $\text{Distance traveled by 'A'} = 1 \, \text{m/s} \times 600 \, \text{s} = 600 \, \text{meters}$ So, at 1:10 p.m., 'A' is already 600 meters ahead of 'B'.

Step 2: Set up the relative motion equation

After 1:10 p.m., both 'A' and 'B' are moving. 'B' has to cover the 600-meter gap between them.

• The relative speed between 'B' and 'A' is: $\text{Relative speed} = 2 \, \text{m/s} - 1 \, \text{m/s} = 1 \, \text{m/s}$

Step 3: Calculate the time for 'B' to meet 'A'

To catch up, 'B' needs to cover the 600-meter distance at the relative speed of 1 m/s. The time taken for this is: $\text{Time taken} = \frac{\text{Distance}}{\text{Relative speed}} = \frac{600 \, \text{m}}{1 \, \text{m/s}} = 600 \, \text{seconds} = 10 \, \text{minutes}$

Step 4: Calculate the distance from point P

In these 10 minutes, 'B' is traveling at 2 m/s. So, the distance covered by 'B' from the starting point P to the meeting point Q is: $\text{Distance} = 2 \, \text{m/s} \times 600 \, \text{s} = 1200 \, \text{meters}$

Thus, the distance between P and Q is 1200 meters.

Final Answer:

The distance between location P and location Q is 1200 meters.

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Do you want any more details on this solution?
Here are 5 related questions to explore:

1. How does the result change if 'B' starts at a different time?
2. What happens if both 'A' and 'B' travel at the same speed?
3. What if 'A' started 15 minutes earlier instead of 10 minutes?
4. How would the problem change if 'B' had a varying speed?
5. How long will it take if both 'A' and 'B' double their speeds?

Tip: In relative motion problems, always subtract the speeds when objects are moving in the same direction.