Yolanda and Yoko ran in a 100-yd dash...

Question

a. 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? b. Assume 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?

Answer 1

Distance = rate x time

 

Yolanda ran 100 yards in 15 seconds , so her speed is 100/15 = 20/3 = 6 and 2/3 yards per second. 

 

Yoko ran 90 yards in 15 seconds, so her speed is 90/15 = 6 yards per second.

 

FOr the second race, Yolanda ran 110 yards at the same speed. So it will take her 110/ (6 and 2/3) =

  110 / (20/3) = 110*3/20  <---- dividing fractions, KFC: keep, change, flip

                     330/20 = 33/2 = 16.5 seconds

 

Yoko runs 100 yards at the same speed. So it will take her 100/6 = 50/3 = 16 and 2/3 seconds.

 

Yolanda will will the second race by 16 2/3 - 16 1/2 =16  4/6 - 16 3/6 = 1/6 seconds or 0.16666..... seconds

                                                                                                                                 = 0.16 seconds 

 

despite the head start.

 

In order to finish in a tie, the times must be the same.

 

Let x be the head start given to Yoko so that they tie.

 

time = distance/rate

 

100 + X                      100

---------------   =   -----------------

  6 and 2/3                      6

 

Cross multiplies  6 ( 100 + x ) =  100 * (6 and 2/3)

 

                       600 + 6x = 2000/3

 

                  1800 + 18X = 2000

 

              18x = 200

 

               x = 200/18 = 100/9 = 11 1/9

 

So if Yoko has 11 1/9 yards head start, they should tie on the next race.

 

Check:  111 and 1/9 = (6 and 2/3) * t

            1000/9 divided by 20/3 = t

            1000/9 * 3/20 = t  <---- KFC: keep , change flip

 

            50/3 = t <--- 16 and 2/3 seconds <--- Yolanda will run 111 and 1/9 yards in 16 and 2/3 seconds

 

           100 = 6 * t

           100/6 = t

           50/3 = t  <---- Yoko will run 100 yards in 16 and 2/3 seconds