Question 1000650: Yolanda and Yoko ran in a 100-yd dash. When Yolanda crossed the finish line, Yoko was 10 yards behind her. The girls then repeated the race, with Yolanda starting 10 yd behind the starting line. If each girl ran at the same rate as before, who won the race? By how many yards?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! yolanda runs 100 yards in the same time that yoko runs 90.
the ratio of yolanda's distance to yoko's distance in the same time is therefore 100 / 9 = 10/9.
you can use this ratio to determine the number of yards that yoko runs in the same time that yolanda runs 110 yards.
if they run at the same speed, then the ratio remains the same, no matter how many yards they run.
you get:
10/9 = 110/x
cross multiply to get 10x = 9 * 110
divide both sides by 10 to get x = 9 * 110 / 10
simplify this to get x = 9 * 11 = 99 yards.
in the same time that yolanda runs 110 yards, yoko runs 99.
looks like yolanda wins again, but by 1 yard this time.
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