Q12. - Algebra 1

Question

The time it takes to complete a go-cart racecourse is inversely proportional to the average speed of the go-cart. One rider has an average speed of 73.3 feet per second and completes the course in 30 seconds. Another rider completes the course in 25 seconds. What was the average speed of the second rider?

Step-by-Step Solution

Answer

The average speed of the second rider is 87.96 feet per second.

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 $\left(x_2,y_2\right)$ 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.

	1st rider	2nd rider
x	73.3	?
y	30	25

 

To find $x_2$, apply product rule for Inverse variation. Substitute 73.3 for $x_1$, 30 for $y_1$, and 25 for $y_2$ into the equation $x_1{y}_1=x_2{y}_2$.

$$\begin{gathered} x_1{y}_1=x_2{y}_2 \\ \left(73.3\right)\times \left(30\right)=\left(x_2\right)\times \left(25\right) \end{gathered}$$

Step 3. Simplify for x 2 .

Further, simplify by dividing both sides by 25.

$$\begin{gathered} \left(73.3\right)\times \left(30\right)=\left(x_2\right)\times \left(25\right) \\ 2199=25x_2 \\ x_2=\frac{2199}{25} \\ x_2=\text{87.96} \end{gathered}$$

Hence, the average speed of the second rider is 87.96 feet per second.