Final answer:
Susan and Daphne will complete a lap around the track at the same time every 12 minutes, as 12 is the Least Common Multiple of their individual lap times, 4 and 6 minutes respectively.
Step-by-step explanation:
To determine when Susan and Daphne will complete a lap around the track at the same time, we need to find the Least Common Multiple (LCM) of their lap times. Susan can walk around the track in 4 minutes, and Daphne can walk around the track in 6 minutes.
The multiples of Susan's lap time (4 minutes) are: 4, 8, 12, 16, 20, 24, ...
The multiples of Daphne's lap time (6 minutes) are: 6, 12, 18, 24, 30, ...
The first common multiple of both sets is 12 minutes. So, Susan and Daphne will complete a lap around the track at the same time every 12 minutes.