Michael and mateo begin running around a circular track from the starting point at the same time. it takes Michael 48 seconds one lap around the track. it takes mateo 60 seconds to complete one lap around the track
how many minutes does it take before the two boys will meet at the starting point again?
how many laps will each boy have run by then?
What is the least common multiple of 48 and 60?
240
so is the first answer 4 minutes?
Ms. Sue????? so is the answer 4 minutes??
Mateo will have run around the track 4 times.
To find out how long it will take for Michael and Mateo to meet at the starting point again, we need to find the least common multiple (LCM) of their lap times. The LCM is the smallest number that is divisible by both lap times.
1. Find the LCM of 48 seconds and 60 seconds.
First, write down the prime factorization of each number:
48 = 2 * 2 * 2 * 2 * 3
60 = 2 * 2 * 3 * 5
Now, multiply the highest powers of all prime factors together:
LCM = 2 * 2 * 2 * 2 * 3 * 5 = 240
So, it will take 240 seconds for Michael and Mateo to meet at the starting point again.
2. Convert seconds to minutes.
We need to convert 240 seconds to minutes. Since there are 60 seconds in a minute, divide 240 by 60.
240 seconds ÷ 60 = 4 minutes
Therefore, it will take 4 minutes for the two boys to meet at the starting point again.
3. Determine the number of laps each boy will have run.
Since Michael takes 48 seconds to complete 1 lap, and they will meet after 240 seconds (4 minutes), we can divide the total time by Michael's lap time:
240 seconds ÷ 48 seconds per lap = 5 laps for Michael
Similarly, since Mateo takes 60 seconds to complete 1 lap, and they will meet after 240 seconds (4 minutes), we can divide the total time by Mateo's lap time:
240 seconds ÷ 60 seconds per lap = 4 laps for Mateo
Therefore, Michael will have run 5 laps and Mateo will have run 4 laps when they meet at the starting point again.