Question

Eric, Fiona, and George stand at the starting line of a running track and begin running laps at the same time. Eric runs one lap every 4 minutes, Fiona runs one lap every 5 minutes, and George runs one lap every 6 minutes. After they start, how long will it take for all three runners to be back at the starting line at the same time?

Answer 1

To find the time it will take for all three runners to be back at the starting line simultaneously, we calculate the Least Common Multiple of their lap times: 60 minutes.

Step-by-step explanation:

To determine how long it will take for Eric, Fiona, and George to be back at the starting line at the same time, we need to find the Least Common Multiple (LCM) of their lap times. Eric's lap time is 4 minutes, Fiona's is 5 minutes, and George's is 6 minutes.

To find the LCM of 4, 5, and 6, we first list some multiples of each number:

• Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...
• Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ...
• Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...

The smallest multiple that is common to all three numbers is 60. Therefore, it will take 60 minutes for all three runners to be back at the starting line at the same time.