Sophie and Claire are having a foot race. Claire is given a 100-foot head-start. If Sophie is runn

Sophie and Claire are having a foot race. Claire is given a 100-foot head-start. If Sophie is running at 5 feet per second and Claire is running at 3 feet per second.
i. After how many seconds will Sophie catch Claire?
ii. If the race is 500 feet, who wins?


i.
Sophie's distance formula is given as D = 5s
Claire's distance formula is given as D = 3s + 100

Set them equal to each other
5s = 3s + 100

Subtract 3s from both sides:
2s = 100

Divide each side by 2
s = 50

ii. Sophie since after 50 seconds, she takes the lead and never gives it back.