Two cyclists begin training on an oval racecourse at the same time. The…
2024
Two cyclists begin training on an oval racecourse at the same time. The professional cyclist completes each lap in 4 minutes; the novice takes 6 minutes to complete each lap. How many minutes after the start will both cyclists pass at exactly the same spot where they began to cycle?
- A.
10
- B.
8
- C.
14
- D.
12
Attempted by 1863 students.
Show answer & explanation
Correct answer: D
Solution: Determine the first time both cyclists are at the starting point together.
Both cyclists are at the starting point exactly when each has completed an integer number of laps, so the time must be a common multiple of 4 minutes and 6 minutes.
Professional cyclist: completes a lap every 4 minutes → time must be a multiple of 4.
Novice cyclist: completes a lap every 6 minutes → time must be a multiple of 6.
Find the least common multiple (LCM) of 4 and 6 to get the first time this happens.
gcd(4, 6) = 2, so LCM = 4 × 6 ÷ 2 = 12 minutes.
Check: In 12 minutes the professional completes 12/4 = 3 laps and the novice completes 12/6 = 2 laps, so both are at the starting point together for the first time.
Answer: 12 minutes.