math urgent help!!!

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?

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  1. 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

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  2. thnx 4 hlping!!!!! but one more question, i didn't understand the last part of the explanation. how many yrds did yolanda win by?

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  3. 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

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  4. Yolanda= 100/time
    So yolanda Wins yoko by 1yard

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