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

Question

b. Assuming the girls run at the same rate as before, how far behind the starting line should Yolanda be in order for the two to finish in a tie?

(please explain i don't get this!)

Answer 1

Yoko's speed is 9/10 of Yolanda's

in the time it takes Yolanda to run 110 yd, Yoko runs 99 yd

so Yolanda wins the second race by a yard

for a tie, the 100 yd that Yoko runs must be 9/10 of the distance that Yolanda runs

.9 x = 100 __ x = 1000/9

Yoko runs 100 yd (900/9); and Yolanda runs an extra 100/9 yd (11 yd 4 inches)