Florian ran 1.2 miles and walked 4.8 laps around the path at the park for a total distance of 3.6 miles. Which shows the correct equation and value of [tex]$x$[/tex], the distance of 1 lap around the path at the park?
A. [tex]3.6x + 1.2 = 4.8; x = 1[/tex] mile
B. [tex]4.8x + 1.2 = 3.6; x = 0.5[/tex] mile
C. [tex]3.6x + 1.2 = 4.8; x = 0.5[/tex] mile
D. [tex]4.8x + 1.2 = 3.6; x = 0.5[/tex] mile
Answer (1)
Define x as the distance of one lap.
Formulate the equation: 1.2 + 4.8 x = 3.6 .
Solve for x : 4.8 x = 2.4 .
Find the value of x : x = 0.5 mile.
Explanation
Understanding the Problem Let's analyze the problem. Florian ran 1.2 miles and walked 4.8 laps around the path. The total distance is 3.6 miles. We need to find the correct equation and the value of x , where x is the distance of 1 lap around the path.
Setting up the Equation Let x be the distance of 1 lap around the path. The total distance Florian walked is 4.8 x miles. The total distance Florian ran and walked is 1.2 + 4.8 x miles.
Formulating the Equation We know that the total distance is 3.6 miles, so we have the equation 1.2 + 4.8 x = 3.6
Solving for x Subtract 1.2 from both sides of the equation: 4.8 x = 3.6 − 1.2 4.8 x = 2.4
Calculating the Value of x Divide both sides by 4.8 to solve for x :
x = 4.8 2.4 = 0.5 mile.
Conclusion Therefore, the correct equation is 4.8 x + 1.2 = 3.6 and the value of x is 0.5 mile.
Examples
Imagine you are planning a track event. Knowing how to calculate the length of each lap ( x ) is crucial for setting up the course correctly. If you know the total distance of the race and how much of it is covered by running straight versus laps around the track, you can use this method to find the exact length of each lap. This ensures fair and accurate measurements for all participants.
