Question

A) Yolanda and yoko ran a 100-yard dash. When Yolanda crossed the finish line, Toko was 10 yards behind her. Then the girls ran again and Yolanda started from 10 yards behind the starting line. If each girl ran at the same speed as before, who won the race? By how many yards of difference? b) Assuming the girls run at the same speed as before, how many yards behind the starting line does Yolanda have to go for the race to end in a draw?

Answer 1

For Yolanda

Let Yolande speed = x

Speed = Distance / Time

Time = Distance / Speed

Time = 100/x

For Toko

Let Toko speed = y

Speed = Distance / Time

Time = Distance / Speed

Time = 100/y

For the remaining 10 yard

Time = 10/y

Therefore,

`\begin{gathered} (100)/(y)\text{ - }(100)/(x)\text{ = }(10)/(y) \\ (10)/(y)\text{ - }\frac{10}{x\text{ }}\text{ = }(1)/(y) \\ (10)/(y)\text{ - }(1)/(y)\text{ = }(10)/(y=x) \\ (9)/(y)\text{ = }(10)/(x) \\ 10y\text{ = 9x} \\ y\text{ = }(9x)/(10) \\ y\text{ = 0.9x} \end{gathered}`

Yolanda started from 10 yards behind the starting line.

Toko distance = 90 yards

Yolanda distance = 100 yards

Toko Time

`\begin{gathered} \text{Speed = }\frac{Dis\tan ce}{\text{Time}} \\ \text{Time = }\frac{Dis\tan ce}{\text{Speed}} \\ \text{Time = }(90)/(0.9x) \\ \text{Time = }(100)/(x) \end{gathered}`

Yolanda Time

`\begin{gathered} \text{Speed = }\frac{Dis\tan ce}{\text{Time}} \\ \text{Time = }\frac{Dis\tan ce}{\text{Speed}} \\ Time\text{ = }(100)/(x) \end{gathered}`

Since they cross the line at the same time

Hence, the race ended in a draw.

b) Yolanda needs to be 10-yards behind the starting line for the race to end in a draw.