two runners jog around an oval path at constant rates, but in opposite directions. 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 your answer as a mixed number.
What's the LCM of 10 and 12?
To determine the time between consecutive meetings of the runners, we need to find the least common multiple (LCM) of 10 and 12.
To find the LCM, we can list the multiples of each number until we find a common multiple. Let's start with 10:
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120...
Now let's list the multiples of 12:
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120...
You can see that the first common multiple is 60 (both 10 and 12 are divisible by 60). Therefore, the runners will meet every 60 minutes.
However, the question asks us to express the answer as a mixed number. To do this, we divide 60 by the sum of the runners' lap completion times.
10 + 12 = 22
Dividing 60 by 22, we get:
60 ÷ 22 = 2 remainder 16
So the runners will meet every 2 and 16/22 minutes.
Simplifying the fraction 16/22:
16/22 = 8/11
Therefore, the runners will meet every 2 and 8/11 minutes.