To determine how many miles John runs per hour, we can start by solving the equation given in the proportional relationship:
\[ 4y = 26.2x \]
In this context:
- \( y \) represents the number of hours he runs (which is 4).
- \( x \) represents the number of miles run (which is 26.2).
We can substitute \( y = 4 \) into the equation:
\[ 4(4) = 26.2x \]
This simplifies to:
\[ 16 = 26.2x \]
Now, solve for \( x \):
\[ x = \frac{16}{26.2} \]
Calculating the above gives us:
\[ x \approx 0.609 \]
Since we want to find the miles per hour, we can simply divide the total miles run by the total hours:
\[ \text{Miles per hour} = \frac{26.2 \text{ miles}}{4 \text{ hours}} = 6.55 \text{ mph} \]
Thus, John runs approximately 6.55 mph.
The correct answer from the choices given is 6.55 mph.
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