Q4. - Algebra 1

Question

Manuel runs an average of 8 miles per hour and finishes a race in 0.39 hours. Dyani finished the race in 0.35 hours. What was her average pace?

Step-by-Step Solution

Answer

The average pace of Dyani is 8.91 miles per hour.

Step 1. State the concept.

Relationship of the form $xy=k$ or $y=\frac{k}{x}$ where $x,y\ne 0$ for some nonzero constant $k$ is known as inverse variation i.e., $y$ varies inversely as $x$.

Product Rule for Inverse Variations – If $\left(x_1,y_1\right)$ and $+$ are solutions of an inverse variation, then $x_1{y}_1=x_2{y}_2$.

Step 2. Apply Product rule for Inverse Variations.

First, make the table representing the situation given.

$x$	Distance	8	$x_2$
$y$	Time (hour)	0.39	0.35

 

In order to find $x_2$, apply the product rule for Inverse variation. Substitute 8 for $x_1$, 0.39 for $y_1$ and 0.35 for $y_2$ into the equation $x_1{y}_1=x_2{y}_2$.

$$\begin{gathered} x_1{y}_1=x_2{y}_2 \\ \left(8\right)\times \left(0.39\right)=\left(x_2\right)\times \left(0.35\right) \end{gathered}$$

Step 3. Simplify for x 2 .

Further, simplify by dividing both sides by 0.35.

$$\begin{gathered} \left(8\right)\times \left(0.39\right)=\left(x_2\right)\times \left(0.35\right) \\ 3.12=0.35x_2 \\ x_2=\frac{3.12}{0.35} \\ x_2=8.91 \end{gathered}$$

Hence, the average pace of Dyani is 8.91 miles per hour.