two runners jog around an oval path at constant rates, but in opposite direstions. one runner completes a lap every 10 minutes, and the other does a lap every 12 minutes. how many minutes elapse between consecutive meetings of the runners? express answer as a mixed number.
The time they meet must be a multiple of 10 AND of 12.
So what is the LCM for 10 and 12 ?
To find the number of minutes that elapse between consecutive meetings of the runners, we can use the concept of finding the least common multiple (LCM) of their lap times.
The first runner completes a lap every 10 minutes, while the second runner completes a lap every 12 minutes. To find the LCM of these two numbers, we can list out their multiples:
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, ...
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, ...
From the list, we can see that the first time their lap times coincide is at 60 minutes, where both runners complete 6 laps. Therefore, 60 minutes elapse between consecutive meetings of the runners.
To express this answer as a mixed number, we divide 60 by 10 (the lap time of the first runner) to find the number of laps completed by the first runner, which is 6. The remainder is 0, indicating that the second runner has also completed 6 laps. Therefore, the answer is 6 and 0/1, or simply 6.
So, the runners meet every 6 minutes.