Question

Four friends, A, B, C and D, decide to jog for 30 minutes inside a stadium with a circular running track that is 200 metres long. The friends run at different speeds. A completes a lap exactly every 60 seconds. Likewise, B, C and D complete a lap exactly every 1 minute 30 seconds, 40 seconds and 1 minute 20 seconds respectively. The friends begin together at the start line exactly at 4 p.m. What is the total of the numbers of laps the friends would have completed when they next cross the start line together?

• A. 36
• B. 52
• C. 42
• D. 48
• E. 47

Hint:

To find when multiple periodic events coincide, find the LCM of the individual periods.

Answer 1

Answer: (E)

Step 1: Times per lap: A = 60 sec, B = 90 sec, C = 40 sec, D = 80 sec.
Step 2: They start together at 4:00. They will next be together at the start line after a time that is the LCM of their lap times.
Step 3: Find LCM of 60, 90, 40, 80. Prime factors: 60 = $2^2 \times 3 \times 5$. 90 = $2 \times 3^2 \times 5$. 40 = $2^3 \times 5$. 80 = $2^4 \times 5$. LCM = $2^4 \times 3^2 \times 5 = 16 \times 9 \times 5 = 720$ seconds.
Step 4: In 720 seconds: A completes $\frac{720}{60} = 12$ laps. B completes $\frac{720}{90} = 8$ laps. C completes $\frac{720}{40} = 18$ laps. D completes $\frac{720}{80} = 9$ laps.
Step 5: Total laps = $12 + 8 + 18 + 9 = 47$.
Step 6: Final Answer: The total number of laps completed is 47.