SOLUTION: "Yolanda and Yoko ran in a 100-yd dash. When Yolanda crossed the finish line, Yoko was 10-yd behind her. The girls then repeated the race, with Yolanda starting 10-yd behind the st

Question 271607: "Yolanda and Yoko ran in a 100-yd dash. When Yolanda crossed the finish line, Yoko was 10-yd 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?"
I am a parent who was trying to help her son with his homework. When working on this problem, I had Yolanda running at 100-yd per hour and Yoko at 90-yd per hour. (Just to make the problem easier to solve) My solution has the girls actually meeting up at the 90-yd line, but then Yolanda overtakes Yoko and still wins the race by 1/10 of a yard. However, my son's teacher told him that the girls ended the second race in a tie. Could someone please help me with this? Thank You!
Found 2 solutions by mananth, richwmiller:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Yolanda and Yoko ran in a 100-yd dash. When Yolanda crossed the finish line, Yoko was 10-yd 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?"
Let the time taken by both in the first race be t to cover 100 yards and 90 yards by Yolanda and Yoko respectively.
Speed of Yolanda is 100 /t
Speed of Yoko is 90/t
They run at the same speed in the next race.
What is the time taken by each of them to cover their distance?
Time taken by yolanda to cover 110 yards is equal to distance /speed
= 110/(110/t)
= 11t/10
Time taken by Yoko to run 100 yards will be 100/ (90/t)= 10t/9
10/9 is greater than 11/10 so yolanda is faster.
Yolanda covered the race in 11t/10
In 11t/10 yoko will run 90*(11/10) yards
90*(11 /10 ) = 99 yards
So yolanda won by 1 yard.
This appears logical to me.

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
At first glance, it would appear that they would run the second race in a tie.
|__________|Yolanda 100
|_________ |Yoko 90

_|__________|Yolanda 110
|__________|Yoko 100

It should also be obvious that they didn't run the race in one hour so that your calculations might be useful to see who ran faster but can't be used for actual distance covered.
What has changed?
Yoko has to run the full 100 yards to win or tie.
Yolanda has to run 110 yards (10 yards more) to win or tie.
But Yolanda is running faster than Yoko.
If Yolanda running 100/90 (10/9) and Yoko is running 90/90 (1) Yolanda will again run 100 yards while Yoko runs 90
So they will be tied at 10 yards before the finish line not at the finish line for the second race.
Which leaves 10 yards each to finish the race.
But we know that Yolanda is running faster than Yoko. How much faster?
For every 100 yards that Yolanda runs Yoko can run 90 so Yolanda runs 10 for every 9 of Yoko. Since they have ten yards to go, Yolanda will win by one yard.

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