Roger goose had a 500-yard head start on willa. if willa's speed was 40 yards per second and roger's speed was only 20 yards per second, how long did it take willa to catch up

For this case what we should do is write the equation of movement for each person.
 We have then:
 For Roger:
 r = 20 * t + 500
 For Willa:
 r = 40 * t
 Equating the equations:
 20 * t + 500 = 40 * t
 We cleared t:
 40 * t - 20 * t = 500
 20 * t = 500
 t = 500/20
 t = 25 s
 
 it did take willa 25 s to catch up Roger.