Question

Michelle walks every 4 days around her neighborhood and swims every 10 days at the gym for thirty minutes. She did both types of excerise, walking and swimming, on December 7th. What day in December will she do both on the same day again?

Answer 1

Michelle will next walk and swim on the same day again on December 27th, which is found by adding the least common multiple (20 days) of her walking (every 4 days) and swimming (every 10 days) schedules to the last day she did both, December 7th.

Step-by-step explanation:

The subject of this question is Mathematics, specifically dealing with the concept of least common multiples (LCM). To find out on which day in December Michelle will walk and swim on the same day, we must find the LCM of the two frequencies. Since she walks every 4 days and swims every 10 days, we need to find the least common multiple of 4 and 10.

Step 1: List the multiples of each number until we find a common multiple:

• Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, ...
• Multiples of 10: 10, 20, 30, 40, 50, ...

Step 2: The smallest (least) common multiple of 4 and 10 is 20.

Step 3: Since both activities were performed on December 7th, add the LCM of 20 days to December 7th to determine the next day both activities will be done together.

December 7th + 20 days = December 27th.

Hence, Michelle will both walk and swim on the same day again on December 27th.