To determine how many miles John runs per hour, we can use the given proportional relationship represented by the equation \( 4y = 26.2x \).
In this equation, let:
- \( y \) represent the number of hours,
- \( x \) represent the distance in miles.
Since John runs the marathon in 4 hours, we can substitute \( y = 4 \) into the equation:
\[ 4(4) = 26.2x \]
Now simplify the left side:
\[ 16 = 26.2x \]
Next, we solve for \( x \) by dividing both sides of the equation by 26.2:
\[ x = \frac{16}{26.2} \]
Calculating the fraction:
\[ x \approx 0.6091 \]
This means that John runs approximately \( 0.6091 \) miles in 1 hour.
To find the exact miles per hour he runs, we can also calculate the average speed directly:
\[ \text{Miles per hour} = \frac{\text{Total miles}}{\text{Total hours}} = \frac{26.2 \text{ miles}}{4 \text{ hours}} = 6.55 \text{ miles per hour} \]
So, John runs approximately \( 6.55 \) miles per hour.
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