I need serious help with this problem. it is making me pukk my hair out!!!
Yolanda and Yoko ran in a 100-yd dash. When Yolanda crossed the finish line, Yoko was ten yd behind her. The girls then repeated the race, with Yolanda starting 10 yd behing the starting line. If each girl ran at the same rate as before, who won the race? By how many yards?
I said Yoko won by 10 yards. I am pretty sure my answer is wrong. Can someone plz tell me the right answer and how they got it?
first race:
Yolanda ran 100 yd in t sec, so her rate is 100/t yds/sec
Yoko ran only 90 yds in t sec, so her rate is 90/t yds/sec
second race:
Yolanda ran 110 yds at 100/t yds/sec for a time of 110/(100/t) or 1.1t seconds
yoko ran 100 yds at 90/t yds/sec for a time of 100/(90/t) or 1.11111...t sec
since 1.1 t < 1.111t, Yolanda won again
the difference in their times is
│(11/10)t - (10/9)t │ = (1/90)t
which at Yoko's rate gives a distance of
90/t * (1/90)t = 1 yard
thnx 4 hlping!!!!! but one more question, i didn't understand the last part of the explanation. how many yrds did yolanda win by?
1 yard
remember distance = rate*time
Yoko ran (1/90)t seconds longer at her rate of (90/t) yards/sec
so distance = 90/t * (1/90)t
= (90t)/90t) = 1
Yolanda= 100/time
Yoko=90/time
So yolanda Wins yoko by 1yard
To solve this problem, we need to find out who won the race and by how many yards.
Let's first calculate the distance covered by Yolanda in the first race. It is mentioned that when Yolanda crossed the finish line, Yoko was ten yards behind her. Therefore, Yolanda covered 100 yards in the first race.
In the second race, Yolanda starts ten yards behind the starting line. This means that Yolanda needs to cover 100 + 10 = 110 yards to reach the finish line.
Since both Yolanda and Yoko run at the same rate as before, we can compare the distances they need to cover in the second race. Yolanda needs to cover 110 yards, while Yoko needs to cover 100 yards.
However, Yolanda starts ten yards behind, so she effectively has a head start. This means that Yolanda will win the race if she reaches the finish line before Yoko catches up to her head start distance of ten yards.
Since Yolanda is running at the same rate, it would take Yoko the same amount of time to cover ten yards as it would take Yolanda to cover 110 - 10 = 100 yards. Therefore, Yolanda will win the race by 100 - 10 = 90 yards.
So, the correct answer is that Yolanda won the race by 90 yards.
Note: It's essential to carefully read and understand the problem while paying attention to the details provided to find the correct solution.