1.

x + 1 = y

Where x is how many laps Brent walked and y how many Diane walked

x = (1/24)m and y = (1/20)m, where m is the number of minutes they've walked

(5/6)y = (1/24)m = x

(5/6)y + 1 = y

(1/6)y = 1

y = 6

Therefore Diane lapped brent after 6 laps.

6 * 20 = 120 minutes.