peter sam and ben run on a circular track. peter takes 100 sconds and ben takes 120 seconds to complete one round. if they start together when will they meet again?
Answers
Correct Question:
Peter, Sam and Ben run on a circular track. Peter takes 100 seconds, Sam takes 110 and Ben takes 120 seconds to complete one round. If they start together, when will they meet again?
Given:
✰ Time taken by Peter to complete one round = 100 s
✰ Time taken by Sam to complete one round = 110 s
✰ Time taken by Ben to complete one round = 120 s
To find:
✠ When will they meet again?
Solution:
Let's understand the concept first! Here we will find L.C.M of 100, 110 and 120 by prime factorization method. There L.C.M will be the time when they meet again.
How to take find L.C.M by prime factorization:
- Find the prime factors of each given number.
- The factor which is common in all, write it once and the other factors as it is.
- Multiply these factors to get the L.C.M of the given numbers.
Let's find out...♪
➛ Prime factors of 100 = 2 × 2 × 5 × 5
➛ Prime factors of 110 = 2 × 5 × 11
➛ Prime factors of 120 = 2 × 2 × 2 × 3 × 5
Now,
➣ Required time = L.C.M of 100, 110 and 120
➣ Required time = 2 × 5 × 2 × 5 × 11 × 2 × 2 × 3
➣ Required time = 100 × 11 × 2 × 2 × 3
➣ Required time = 100 × 132
➣ Required time = 13200 sec
Convert it into minutes,
➛ 1 sec = 1/60 min
➛ 13200 sec = 13200/60 min
➛ 1320/6 min
➛ 220 min
∴ Time when they will meet again = 220 min
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✰ Time taken by Peter to complete one round = 100 s
✰ Time taken by Sam to complete one round = 110 s
✰ Time taken by Ben to complete one round = 120 s
To find:
✠ When will they meet again?
Solution:
Let's understand the concept first! Here we will find L.C.M of 100, 110 and 120 by prime factorization method. There L.C.M will be the time when they meet again.
How to take find L.C.M by prime factorization:
Find the prime factors of each given number.
The factor which is common in all, write it once and the other factors as it is.
Multiply these factors to get the L.C.M of the given numbers.
Let's find out...♪
➛ Prime factors of 100 = 2 × 2 × 5 × 5
➛ Prime factors of 110 = 2 × 5 × 11
➛ Prime factors of 120 = 2 × 2 × 2 × 3 × 5
Now,
➣ Required time = L.C.M of 100, 110 and 120
➣ Required time = 2 × 5 × 2 × 5 × 11 × 2 × 2 × 3
➣ Required time = 100 × 11 × 2 × 2 × 3
➣ Required time = 100 × 132
➣ Required time = 13200 sec
Convert it into minutes,
➛ 1 sec = 1/60 min
➛ 13200 sec = 13200/60 min
➛ 1320/6 min
➛ 220 min
∴ Time when they will meet again = 220 min
_______________________________