Question

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 1

Yolanda wins the race by 1 yard.

Explanation:

Yolanda runs,

100 yard in 15 second

so 1 yard in
`(15)/(100)` second

or (100 + 10) = 110 yard in
`(15 * 110)/(100)` second

=
`16(1)/(2)` second

Yoko runs, (100 - 10) yard = 90 yard in 15 seconds

so, 1 yard in
`(15)/(90)` second

so, 100 yard in

`(15 * 100)/(90)` second

=
`16(2)/(3)` second

Since ,

`16(1)/(2)` <
`16(2)/(3)`

so, Yolanda wins the race.

Yoko runs
`(90)/(15)` yard per second

= 6 yard per second

and in (
`16(2)/(3)` -
`16(1)/(2)`) seconds

=[tex]\frac{1}{6}[/tex] seconds

Yoko runs,
`(6)/(6)` yard = 1 yard

So, Yolanda wins the race by 1 yard.