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.

A. 7 mph
B. 104.8 mph
C. 6.55 mph
D. 0.15 mph

3 answers

To find out how many miles John runs per hour, we first need to solve the equation given in the problem, \( 4y = 26.2x \).

In this equation, \( y \) represents the speed in miles per hour (mph) and \( x \) represents the time in hours.

We're told that John runs for 4 hours, so we can substitute \( x = 4 \) into the equation:

\[ 4y = 26.2 \cdot 4 \]

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

\[ 26.2 \cdot 4 = 104.8 \]

Now, we have:

\[ 4y = 104.8 \]

To find \( y \), we divide both sides by 4:

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

Now, to determine the speed:

Using the speed formula which is distance divided by time, we can also confirm:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{26.2 \text{ miles}}{4 \text{ hours}} = 6.55 \text{ mph} \]

Thus, the correct answer is:

C. 6.55 mph

are you sure this is correct

Let me re-evaluate the problem and confirm the calculations step by step.

The equation provided is:

\[ 4y = 26.2x \]

In this equation, \( y \) stands for the speed in miles per hour, and \( x \) represents the time in hours. Since John runs the marathon in 4 hours, we substitute \( x = 4 \) into the equation:

\[ 4y = 26.2 \cdot 4 \]

Calculating \( 26.2 \cdot 4 \):

\[ 26.2 \cdot 4 = 104.8 \]

So now we have:

\[ 4y = 104.8 \]

To solve for \( y \):

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

Now, we should recognize that \( y \) gives us the miles he would run in 4 hours. We still need to calculate the speed based on distance and time. The correct measure of speed (in miles per hour) is derived from dividing the total distance by the total running time.

The speed is given by:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{26.2 \text{ miles}}{4 \text{ hours}} = 6.55 \text{ mph} \]

Thus, the calculation of John's speed as 6.55 mph is indeed correct. Therefore, the correct answer remains:

C. 6.55 mph

I appreciate your patience, and I hope this clarification reassures you about the accuracy of the solution!