Yolanda and Yoko ran in a 100-yd dash. When Yolanda crossed the finish line in 15 seconds, Yoko was 10 yards behind her. The girls then repeated the race, with Yolanda starting 10 yards behind the starting line. If each girl ran at the same rate as before, who won the race? By how many yards?

Answer:Yolanda wins the race by 1 yard.Step-by-step explanation:Yolanda runs, 100 yard in 15 second so 1 yard in [tex]\frac{15}{100}[/tex] secondor (100 + 10) = 110 yard in [tex]\frac{15 \times 110}{100}[/tex] second                                              =[tex]16\dfrac{1}{2}[/tex] secondYoko runs, (100 - 10) yard = 90 yard in 15 seconds                                             so, 1 yard in [tex]\frac{15}{90}[/tex] second                                           so, 100 yard in                                              [tex]\frac{15 \times 100}{90}[/tex] second                                              =[tex]16\dfrac{2}{3}[/tex] secondSince , [tex]16\dfrac{1}{2}[/tex]    <    [tex]16\dfrac{2}{3}[/tex]so, Yolanda wins the race.Yoko runs [tex]\frac{90}{15}[/tex] yard per second                 = 6 yard per secondand in   ([tex]16\dfrac{2}{3}[/tex] -    [tex]16\dfrac{1}{2}[/tex]) seconds               =[tex]\frac{1}{6}[/tex] seconds Yoko runs, [tex]\frac{6}{6}[/tex] yard = 1 yardSo, Yolanda wins the race by 1 yard.