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: Understanding the Concept:
The friends cross the start line together at a time which is the Least Common Multiple (LCM) of their individual lap times.
Step 2: Key Formula or Approach:
1. Convert all times to seconds: $A = 60s, B = 90s, C = 40s, D = 80s$.
2. Find $LCM(60, 90, 40, 80)$.
3. Total Laps $= \frac{LCM}{60} + \frac{LCM}{90} + \frac{LCM}{40} + \frac{LCM}{80}$.
Step 3: Detailed Explanation:
$LCM(60, 90, 40, 80) = 720$ seconds.
Laps by A $= 720/60 = 12$.
Laps by B $= 720/90 = 8$.
Laps by C $= 720/40 = 18$.
Laps by D $= 720/80 = 9$.
Total Laps $= 12 + 8 + 18 + 9 = 47$.
Step 4: Final Answer:
The total number of laps is 47.