yolanda and yoko ran in a 100yd dash. when yolanda was done, yoko was 10yds behind. they started again with yolanda 10yds behind the start.

Question

They want to know who won, and by how many yards?

For part B they want to know how far Yolanda should be behind the starting line for them to finish in a tie?

Answer 1

A. Yolanda won by 1 yd

 

B. 11.111..yd

 

Set the speed of yolanda = x, then the speed of yoko = 0.9*x (given by the fact that yolanda finished 100yd when yoko finished only 90yd)

 

A. 110yd/x = time spend by yolanda to finish his 110yads (set the value = t),

 

     with the same time yoko only finished t*0.9*x= 110yd/x*0.9*x=99yd  therefore yolanda won by 1yd

 

B. For them to finish in tie, set s = the distance yolanda shall finish when yoko finishes 100yd

   

     So we have:  s/x=100yd/(0.9*x), s=100yd/0.9=111.11...yd,

     so yolanda shall start 111.11...yd-100yd=11.11...yd behind the line for them to finish in a tie!