Yolanda and Yoko ran in 100 yd dash. When Yolanda crossed the finish line, Yoko was 10 yrd behind her. The girls then repeated the race, with Yolanda starting 10 yrd behind the starting line. If each girl ran at the same rate as before, who won the race? By how many yards?
i say it would be a tie
next question:
Assuming the girls run at the same rate as before, how far behind the starting line should Yolanda be in order for the 2 to finish in a tie?
10 yards
First race:
let Yolanda' time to finish the 100 yds be t sec
then Yolanda's rate = 100/t yds/sec
Yoko's rate = 90/t yds/sec
Second Race
Distance for Yolanda is 110 yrd
Distance for Yoko is 100 yrd
time to run for Yolanda to run 110 yrs = 110/(100/t) = 1.1 t
time for Yoko to run 100 yrs = 100/(90/t) = 1.1111..t
So when Yolanda has done her 110 yds in 1.1t seconds, Yoko would not be finished yet
So it is not a tie..!!!
let the distance Yolanda should start behind the starting line be x yds
so for the times to be the same..
(100+x)/(100/t) = 100/(90/t)
t(100+x)/100 = t(100)/90
divide by t
(100+x)/100 = 100/90
90(100+x) = 100(100)
9(100+x) = 10(100)
900 + 9x = 1000
9x = 100
x = 100/9 = 11.11111. yds
on part one of the question Yolanda wins by one second I am currently working on the second question.
To analyze the first question, let's break down the scenario step by step:
1. Yolanda and Yoko initially ran in a 100-yard dash.
2. When Yolanda crossed the finish line, Yoko was 10 yards behind her.
Given this information, you are correct to assume that it would be a tie if they repeat the race. Here's why:
1. In the first race, Yolanda finished the 100-yard dash while Yoko was 10 yards behind her.
2. In the second race, Yolanda starts 10 yards behind the starting line.
3. Since both girls run at the same rate as before, if Yolanda starts 10 yards behind, she would finish the race at the same moment that Yoko crosses the finish line.
Therefore, it would indeed be a tie if they repeat the race.
Moving on to the second question:
To find out how far behind the starting line Yolanda should be in order for the two to finish in a tie, we can use the information given.
1. Initially, Yolanda finished the race while Yoko was 10 yards behind.
2. If they are to finish in a tie, Yolanda needs to be positioned in a way that she and Yoko cross the finish line simultaneously.
3. Since Yoko was 10 yards behind Yolanda in the initial race, to achieve a tie, Yolanda should start 10 yards behind the starting line.
By starting 10 yards behind the starting line, both Yolanda and Yoko will finish the race at the same time, resulting in a tie.