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 lapse between consecutive meetings of the runners? Express your answer as a mixed number.
To find out how many minutes lapse between consecutive meetings of the runners, we need to find the time it takes for them to meet again.
Let's first find the time it takes for them to complete one lap together. To do this, we need to find the least common multiple (LCM) of 10 and 12.
To find the LCM, we can list the multiples of 10 and 12 until we find a common multiple:
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, ...
From the lists above, we can see that the least common multiple of 10 and 12 is 60.
So, it takes 60 minutes for both runners to meet again.
However, we need to express the answer as a mixed number. Since 60 is divisible by both 10 and 12, we can express it as a mixed number.
Dividing 60 by 10 gives us 6, which means the first runner will complete 6 laps in 60 minutes.
Dividing 60 by 12 gives us 5, which means the second runner will complete 5 laps in 60 minutes.
Therefore, the runners will meet after the first runner completes 6 laps and the second runner completes 5 laps.
Since they jog in opposite directions, the number of meetings will be one less than the number of laps completed by the faster runner (the one who completes a lap every 10 minutes).
So, the runners will meet after 5 meetings.
To find the total time lapse between the consecutive meetings, we multiply the number of meetings by the time it takes for them to meet again: 5 meetings * 60 minutes = 300 minutes.
Therefore, there will be 300 minutes lapse between consecutive meetings of the runners.