Question

Behrgan and McKenna are riding bikes around the neighborhood loop. It takes Behrgan 2.4 minutes to get around the loop, and McKenna takes 1.6 minutes. If they both start riding from the same spot at the same time, when do they meet at the start spot again? Please explain the solution.

Answer 1

To find when Behrgan and McKenna meet at the start spot again, we calculate the least common multiple (LCM) of their lap times of 2.4 minutes and 1.6 minutes, respectively. The first common multiple of their times is 9.6 minutes, thus they will meet after 9.6 minutes.

Step-by-step explanation:

To determine when Behrgan and McKenna meet at the start spot again, we need to find the least common multiple (LCM) of their lap times. Behrgan's lap time is 2.4 minutes and McKenna's lap time is 1.6 minutes.

First, we express the times as fractions of a minute to make it easier to calculate the LCM: Behrgan's time is ⅕12 minutes (since 2.4 minutes = ⅕⅒⅞ minutes) and McKenna's time is ⅕8 minutes (since 1.6 minutes = ⅕⅖⅞ minutes).

Next, we list the multiples of each time until we find a common multiple:

• 
  
• Multiples of ⅕12: 2.4, 4.8, 7.2, 9.6, 12, ...
• 
  
• Multiples of ⅕8: 1.6, 3.2, 4.8, 6.4, 8, 9.6, ...

The first common multiple we see is 9.6 minutes. Therefore, Behrgan and McKenna will meet back at the start spot after 9.6 minutes.