There will be a total of 12 times at which at least two sisters run together during May.
Step-by-step explanation:
Step 1:
The month of May starts on a Friday and has 31 days.
Kate runs every alternate day, Lottie runs on every third day while Miriam runs only on Saturdays and Sundays.
As Kate and Lottie already ran together on the last day of April, Kate will run on every even day of May i.e. 2, 4, 6, 8 ... 30.
Lottie will run on days that are multiples of 3 i.e. 3, 6, 9 ... 30.
As Miriam only runs on weekends, she runs on May 1, 2, 8, 9, 15, 16, 22, 23, 29, and 30.
Step 2:
First, we check the number of times all three sisters ran together.
These are the multiples of 2 and 3 that come on May 1, 2, 8, 9, 15, 16, 22, 23, 29, and 30 (the days that Miriam runs).
The day that all three sisters run together is only May 30.
The days that are multiples of 2 or 3 that come on weekends are; 2, 8, 9, 15, 16, 22, and 30. So 7 days in this category.
The days that are both multiples of 2 and 3 are; 6, 12, 18, 24 (30 has already been counted). So 4 days under this category.
So the number of times at least two sisters will run together = [tex]7 +5 =12.[/tex]So they will run together on 12 days in May.
