CIRCULAR TRACK & MEETING PROBLEMS
CORE CONCEPT
When two or more people move on a circular track, they start from the same point and move in the same or opposite directions. We need to find when they meet again, how many times they meet, or their relative speeds. This is different from linear track problems because the track repeats — people can meet multiple times at different points.
KEY RULES & PROPERTIES
1. Same Direction Meeting: Person A and B start together.
A is faster. A will lap (overtake) B when A covers exactly one full lap MORE than B. They meet again when the faster person gains a full circle's distance on the slower one.
2. Opposite Direction Meeting: They are moving towards each other.
They meet every time their combined distance equals the track length.
3. Relative Speed Concept: In same direction, relative speed = (Speed of faster person) - (Speed of slower person). In opposite direction, relative speed = (Speed of person 1) + (Speed of person 2).
4. Time Between Meetings: This stays constant for each meeting if speeds are constant.
FORMULA BLOCK
Same direction (A catches B):
• Time to meet = Track Length / (Speed of A - Speed of B)
• In n meetings, faster person covers n × Track Length more than slower person
Opposite direction:
• Time to first meeting = Track Length / (Speed A + Speed B)
• They meet again at same time intervals after the first meeting
EXAM PATTERNS
1. Two persons on circular track, find when they meet next
2.
How many times do they meet in a given time?
3. At what point on the track do they meet?
4. Relative speed and time calculation problems
SHORTCUT/TRICK
"For same direction problems: Just find how long it takes for the faster person to gain one full lap.
That's your meeting time. Multiply by the number you need."
WORKED EXAMPLE
A and B run on a 400m circular track. A's speed is 10 m/s and B's speed is 6 m/s.
Both start together from the same point in the same direction. When will they meet again?
Step 1: Since they're moving in the same direction, relative speed = 10 - 6 = 4 m/s
Step 2: For A to meet B again, A must gain exactly one full lap = 400m
Step 3: Time = Distance / Speed = 400 / 4 = 100 seconds
Step 4: They meet again after 100 seconds.
Verification: In 100 seconds, A covers = 10 × 100 = 1000m = 2 full laps + 200m. B covers = 6 × 100 = 600m = 1 full lap + 200m.
Both are at the same point (200m mark). ✓
COMMON MISTAKE
Students often forget that in SAME direction, you subtract speeds. They wrongly add speeds (which is for opposite direction only). This leads to completely wrong answers.
Always check the direction first.