One trip around a running track is 440 yards. One jogger can complete one lap in 8

Question

minutes, the other can complete in 6 minutes. How long will it take for both joggers to
arrive at their starting point together if they start at the same time and maintain their
jogging pace?

Answer 1

To determine how long it will take for both joggers to arrive at their starting point together, we need to find the least common multiple (LCM) of the times it takes for each jogger to complete one lap around the track.

1. Jogger 1 completes a lap in 8 minutes.
2. Jogger 2 completes a lap in 6 minutes.

Now, we find the LCM of 8 and 6:

• The prime factorization of 8 is \( 2^3 \).
• The prime factorization of 6 is \( 2^1 \cdot 3^1 \).

To find the LCM, we take the highest power of each prime factor:

• For the prime factor 2: The highest power is \( 2^3 \).
• For the prime factor 3: The highest power is \( 3^1 \).

Thus, the LCM is: \[ LCM = 2^3 \cdot 3^1 = 8 \cdot 3 = 24 \]

Therefore, the least common multiple of 8 and 6 is 24 minutes.

This means both joggers will arrive at their starting point together after 24 minutes.