Chapter 6.4, Problem 27IP

To determine

To find: Juliette’s 400-meter dash time.

Answer to Problem 27IP

Juliette’s 400-meter dash time $=x=85.1$ seconds.

Juliette’s 400-meter dash time > Torie’s 400-meter dash time

Explanation of Solution

Given information:

Torie’s 400-meter dash time = Original value $=74$ seconds

Juliette’s time is $15\%$ faster than Torie’s.

It means

Percent of change = $15\%$

Percent of change $=\frac{A}{O}\times 100$

Where

  $A=$ Amount of change.

  $O=$ Original amount.

From given information

Torie’s 400-meter dash time = Original value $=74$ seconds

Juliette’s time is $15\%$ faster than Torie’s.

It means

Percent of change = $15\%$

Let $\text{'}x\text{'}$ be Juliette’s 400-meter dash time that means Final value.

Amount of change = Final value $-$ Original value

  $\Rightarrow A=x-74$

Therefore,

Percent of change $=\frac{x-74}{74}\times 100$

  $\begin{array}{l}\Rightarrow 15=\frac{100x-7400}{74}\\ \Rightarrow 100x-7400=15\times 74\\ \Rightarrow 100x-7400=1110\\ \Rightarrow 100x=1110+7400\\ \Rightarrow 100x=8510\\ \Rightarrow x=\frac{8510}{100}\\ \Rightarrow x=85.1\end{array}$

Therefore,

Juliette’s 400-meter dash time $=x=85.1$ seconds.

On comparing with

Torie’s 400-meter dash time

We get

Juliette’s 400-meter dash time > Torie’s 400-meter dash time