Yolanda and Yoko ran in 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?

b. Assuming the girls run at the same rate as before, how far behind the starting line should Yolanda be in order for the two to finish in a tie?

(please explain i don't get this!)

Yoko's speed is 9/10 of Yolanda's

in the time it takes Yolanda to run 110 yd, Yoko runs 99 yd

so Yolanda wins the second race by a yard

for a tie, the 100 yd that Yoko runs must be 9/10 of the distance that Yolanda runs

.9 x = 100 __ x = 1000/9

Yoko runs 100 yd (900/9); and Yolanda runs an extra 100/9 yd (11 yd 4 inches)

To solve this problem, let's break it down step by step:

1. First, let's determine the relative speed ratio of Yolanda and Yoko based on the first race. We know that Yoko was 10 yards behind Yolanda when she crossed the finish line. Since it was a 100 yard dash, Yoko was running at 90% of Yolanda's speed (10 yards behind out of 100 yards total).

2. In the second race, Yolanda starts 10 yards behind the starting line. Since Yoko's speed is 90% of Yolanda's, this means Yoko would need to run 110 yards (100 yards for the race distance, plus the extra 10 yards that Yolanda was behind at the start) to complete the race.

3. Now, let's compare the distances each girl would run in the second race. Yolanda would run 100 yards, while Yoko would run 110 yards.

4. Based on their speeds from the first race, Yoko would cover 90% of the distance Yolanda covers in the same time. In the second race, Yolanda runs 10 yards less than Yoko, but both cover the same distance from their respective starting points.

5. Therefore, if each girl ran at the same rate as before, Yolanda would win the race. Yolanda reaches the finish line after running 100 yards, while Yoko would still have 10 more yards to go.

So, Yolanda wins the race by 10 yards.

b. Now, let's determine how far behind the starting line Yolanda should be in order for both girls to finish in a tie.

Since Yolanda runs at a constant speed, she covers 100 yards in the time it takes Yoko to cover 90 yards. To finish in a tie, Yolanda needs to run the same distance as Yoko in the same time.

In the second race, Yoko runs 110 yards. To finish in a tie, Yolanda should also run 110 yards but starting 10 yards behind the starting line.

Therefore, Yolanda should be 10 yards behind the starting line to finish the race in a tie with Yoko.