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

.(1 point)
Responses

7 mph
7 mph

6.55 mph
6.55 mph

104.8 mph
104.8 mph

0.15 mph

1 answer

To determine how many miles John runs per hour, we need to analyze the equation given, which is \(4y = 26.2x\).

In this equation:

  • \(y\) represents the miles per hour (mph).
  • \(x\) represents the number of hours.

Since John runs for \(4\) hours, we can set \(x = 4\) and solve for \(y\).

  1. Substitute \(x = 4\) into the equation: \[ 4y = 26.2 \times 4 \]

  2. Calculate \(26.2 \times 4\): \[ 26.2 \times 4 = 104.8 \]

  3. Now, substitute this into the equation: \[ 4y = 104.8 \]

  4. To find \(y\), divide both sides by \(4\): \[ y = \frac{104.8}{4} \] \[ y = 26.2 \]

Since \(y\) represents the total distance in miles, we need to find the speed in miles per hour: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{26.2 \text{ miles}}{4 \text{ hours}} = 6.55 \text{ mph} \]

Thus, John runs at a speed of 6.55 mph.

The correct response is: 6.55 mph.