john runs a marathon (26.2) in 4 hours. determine how many miles he runs per hour if the proportional relationship is represented by 4y = 26.2x

1 answer

To determine how many miles John runs per hour, we start with the given relationship represented by the equation \(4y = 26.2x\).

Here, \(x\) is the time in hours, and \(y\) is the distance in miles. Since John runs for 4 hours to complete the marathon, we can substitute \(x = 4\) into the equation to find \(y\):

\[ 4y = 26.2 \cdot 4 \]

Now, calculate \(26.2 \cdot 4\):

\[ 26.2 \cdot 4 = 104.8 \]

Therefore, the equation becomes:

\[ 4y = 104.8 \]

Next, divide both sides of the equation by 4 to solve for \(y\):

\[ y = \frac{104.8}{4} = 26.2 \]

Since this confirms the original distance of the marathon John runs (26.2 miles), we can find the miles per hour by dividing the distance by the time:

\[ \text{Miles per hour} = \frac{26.2 \text{ miles}}{4 \text{ hours}} = 6.55 \text{ miles per hour} \]

Thus, John runs approximately 6.55 miles per hour.