Two cyclists, X and Y, start from the same point on a circular track of length…
2026
Two cyclists, X and Y, start from the same point on a circular track of length 504 metres but move in opposite directions. Their initial speeds are 9 m/s and 27 m/s, respectively. Each time they meet, X’s speed triples, and Y’s speed reduces to one-third of its previous value. After how much time will they meet for the third time?
Answer: D. 34 sec — ConceptWhen two objects move in opposite directions on a circular track, their relative speed is the sum of their speeds. The time between consecutive…
- A.
32 sec
- B.
28 sec
- C.
22 sec
- D.
34 sec
Attempted by 10 students.
Show answer & explanation
Correct answer: D
Concept
When two objects move in opposite directions on a circular track, their relative speed is the sum of their speeds.
The time between consecutive meetings equals the track length divided by the relative speed during that interval. If speeds change at a meeting, compute the next interval using the new speeds.
Application
Before the first meeting, the relative speed is 9 + 27 = 36 m/s, so the first meeting occurs after 504 ÷ 36 = 14 seconds.
After the first meeting, X has speed 27 m/s and Y has speed 9 m/s. Their relative speed remains 36 m/s, so the second meeting occurs 504 ÷ 36 = 14 seconds later.
After the second meeting, X has speed 81 m/s and Y has speed 3 m/s. Their relative speed is 81 + 3 = 84 m/s, so the third meeting occurs 504 ÷ 84 = 6 seconds later.
Cross-check
The cumulative meeting times are 14 seconds, 14 + 14 = 28 seconds, and 14 + 14 + 6 = 34 seconds. Therefore, they meet for the third time after 34 seconds.