Lani, Sue, and Jill begin jogging around a quarter-mile track at the same time. Lani takes 2 minutes to complete each lap, Sue takes 3 minutes and Jill takes 4 minutes. How long will they have been jogging when they first meet up again at the point where they began? How many laps will each have run at that first meeting?
it takes 12 min (the LCM of the numbers)
divide by their rates to find the number of laps
Is it 12 , the lcm ?
Ohh im sorry, Its 12 😂But thanksss
To find out when Lani, Sue, and Jill will first meet up again at the starting point, we need to find the least common multiple (LCM) of their lap times. The LCM is the smallest number that is divisible by all the given lap times.
Step 1: Find the LCM of 2, 3, and 4
To find the LCM, we can list the multiples of each number until we find a common multiple.
Multiples of 2: 2, 4, 6, 8, 10, ...
Multiples of 3: 3, 6, 9, 12, 15, ...
Multiples of 4: 4, 8, 12, 16, ...
To find the LCM, we look for the first common multiple in these lists. In this case, the LCM is 12.
Step 2: Find the number of laps completed by each person when they first meet up again.
Now that we know the LCM is 12, we can divide it by each person's lap time to find how many laps they will have completed.
Lani: 12 (LCM) ÷ 2 (lap time) = 6 laps
Sue: 12 (LCM) ÷ 3 (lap time) = 4 laps
Jill: 12 (LCM) ÷ 4 (lap time) = 3 laps
Step 3: Find the total time it takes for them to meet up again.
Since Lani takes 2 minutes to complete each lap, the total time Lani spends jogging until they meet again is 2 (minutes) × 6 (laps) = 12 minutes.
Similarly, Sue takes 3 minutes per lap, so Sue will have been jogging for 3 (minutes) × 4 (laps) = 12 minutes.
Jill takes 4 minutes per lap, so Jill will have been jogging for 4 (minutes) × 3 (laps) = 12 minutes.
Therefore, they will have been jogging for a total of 12 minutes when they first meet up again at the starting point. Each of them would have completed 6 laps, 4 laps, and 3 laps respectively.