Question

A-) who won the race? a1)By how many yards of difference? B-) How many yards behind the starting line does Yolanda have to leave for the race to end in a draw?

Answer 1

EXPLANATION

Let's see the facts:

Race = 100-yard

Toko--> 10 yards < Yolanda

Second part:

Yolanda --> 10 yards behind the starting line

If each geil ran at the same speed as the first race, the appropiate relationship is as follows:

Yolanda's speed = 100 yards/race

Yoko's speed = 90 yards/race

Distance= ratex time

For the second race, Yolanda ran 110 yards at the same speed --> So it will take 110/100 = 1.1 times to finish the race.

Yoko runs 100 yards at the same speed so it will take her 100/90= 1.11111... times to finish the run.

As 1.11 is less time than 1.1111, Yolanda will win the race.

b) 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

$\frac{100+x}{100}=\frac{100}{90}$

Multiplying both sides by 100:

$100+x=100\cdot\frac{100}{90}$

Subtracting -100 to both sides:

$x=100\cdot\frac{100}{90}-100$

Simplifying:

$x=111.11111\ldots-100=11.111\ldots$

So, if Yoko has 11.111... head start, they should tie on the next race.