Susan and daphne are participating in a walk-a-thon at the local community college track to raise money. susan can walk around the track in 4 minutes. daphne can walk around the track in 6 minutes. susan and daphne started walking at the same time. how many minutes will it be until they complete a lap at the same time?

12 minutes

Step-by-step explanation:

We know that Susan will walk a lap in 4 minutes

Daphne will do it in 6 minutes

We have to find the Least Common Multiple for the minutes each of them will take, and it is a number that both numbers (4 and 6) will get as a resul of multiplying them by another number.

We are going to write down the miltiples of 4

4, 8, 12, 16, 20, 24,...

Now the multiples of 6

6, 12, 18, 24,...

Now we can see that there are several numbers that are multiples of 4 and also of 6 like in this case 12 and 24, but we are looking for the smallest number that is common for both numbers: in this case it is 12.

The reason to use the Least Common Multiple is that we know that Susan will finish a lap everytime multiples of 4 minutes pass, and Daphne will finish a lap at every multiple of 6 so when they have in common a multiple they both will be finishing a lap, in this case it will be Susan´s third lap and Daphne´s second lap but they will be crossing the starting line at the same time. And at 12 minutes it will be the first time they will complete a lap at the same time.