We are looking for the Least Common Multiple of 8 and 5 since that is how long it will take Lance to meet up with Alicia again after they start at the same position at the beginning of the lap.

The LCM of 8 and 5 is 8 x 5 = 40 minutes.

Apr 2nd, 2015

Sorry, correction on that one. The question was how long will it take Lance to be one lap AHEAD.

So, we need to set up equation to which subtracts the number of laps Alicia walks from the number of laps Lance walks and set that equal to 1.

Let x = how many minutes it takes for Lance to be one lap ahead

The rate Lance walks is 1 lap / 5 minutes

The rate Alicia walks is 1 lap / 8 minutes

So then,

(1/5)x - (1/8)x = 1

x(1/5 - 1/8) = 1

x(8/40 - 5/40) = 1

(3/40)x = 1

x = 40/3 or 13 1/3 minutes or 13 minutes and 20 seconds