# math unit rate question

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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

• math unit rate question -

the answer to question 1 is a tie and how many yards is 0.the answer to the second question is 10 yards behind the finishing line.

• math unit rate question -

so I was correct i got same answer like you

• Not so fast, grasshopper -

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

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