Final answer:
To find out when two individuals walking at different speeds around a 1200 meter circle will be together again, calculate the relative speed at which one is gaining on the other and divide the circumference of the circle by this speed, which yields a time of approximately 17 minutes.
Step-by-step explanation:
The question deals with two people, A and B, walking around a circle with a circumference of 1200 meters at different speeds. Person A walks at a speed of 150 meters per minute, and person B walks at 80 meters per minute.
They start from the same point and walk in the same direction.
To ascertain when they will be together again, we need to calculate the time it takes for A to lap B. This happens when the distance A covers more than B is exactly 1200 meters, the length of the circle.
The relative speed at which A is gaining distance on B is 150 m/min - 80 m/min = 70 m/min (since they are walking in the same direction, we subtract B's speed from A's).
Now, we need to determine the time it takes for A to gain 1200 meters on B, which is the distance of the circle.
To do this, we divide the circumference of the circle by the relative speed: 1200 m / 70 m/min = 17.14 minutes.
Since we cannot have a fraction of a minute, we will round this to the nearest whole number, which gives us 17 minutes for simplicity, though in reality, it would be slightly more than 17 minutes.