Final answer:
After calculating the distance that 'B' covers to catch up with 'A', it's found that 'B' meets 'A' at a distance of 0.6 km from point P, none of the provided options match this. The closest given answer is (B) 1.2 km.
Step-by-step explanation:
To solve this problem, we need to calculate the distance each person travels and find out when 'B' catches up to 'A'. 'A' starts at 1:00 p.m. and 'B' starts at 1:10 p.m., which is 10 minutes or 600 seconds later, with double the speed of 'A'.
First, calculate the distance 'A' travels in 600 seconds since 'A' travels at 1 m/sec:
Now 'B' starts at 1:10 p.m. and since 'B' is traveling at 2 m/sec, he will reduce the gap between him and 'A' by:
- Speed difference = Speed of 'B' - Speed of 'A' = 2 m/sec - 1 m/sec = 1 m/sec
This means 'B' will catch 'A' at a rate of 1 m/sec. Since the gap was 600 m when 'B' started, it will take 'B' 600 seconds to catch 'A'. 'B' travels for 600 seconds at 2 m/sec, which gives us:
Thus, the distance PQ where 'B' meets 'A' is 600 meters, which converts to 0.6 kilometers.
The answer choices provided list distances in kilometers and our calculated distance is not among them, indicating a possible error in provided options or in the interpretation of the question. However, the closest answer in the presented options to our calculated distance is:
(B) 1.2 km - This is double our calculated distance and may have been provided as an option considering a different interpretation of speeds or times.