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
To find the time between consecutive meetings of the two runners, we need to determine the least common multiple (LCM) of their lap times.
The first runner completes a lap every 10 minutes, so the sequence of times for the first runner's laps would be: 10 minutes, 20 minutes, 30 minutes, 40 minutes, ...
The second runner completes a lap every 12 minutes, so the sequence of times for the second runner's laps would be: 12 minutes, 24 minutes, 36 minutes, 48 minutes, ...
To find the LCM of 10 and 12, we can list the multiples of each number until we find a match:
Multiples of 10: 10, 20, 30, 40, 50, 60, ...
Multiples of 12: 12, 24, 36, 48, 60, ...
From the lists above, we see that the first time both runners meet is after 60 minutes, which is the least common multiple (LCM) of 10 and 12.
Therefore, the number of minutes that elapse between consecutive meetings of the runners is 60 minutes, which can also be written as the mixed number 1 hour.