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)

Question

Responses

0.15 mph
0.15 mph

6.55 mph
6.55 mph

7 mph
7 mph

104.8 mph

Answer 1

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

In this case:

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

Since John runs for 4 hours (so \(x = 4\)), we can substitute \(x\) into the equation:

\[ 4y = 26.2 \cdot 4 \]

Calculating the right side:

\[ 4y = 26.2 \cdot 4 = 104.8 \]

Now we solve for \(y\):

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

To find the miles per hour:

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

Thus, the correct answer is:

6.55 mph.

Answer 2

The proportional relationship 15.24 centimeters in 6 inches is represented by 6y=15.24x. Determine the number of centimeters in 1 inch.(1 point)
Responses

3 centimeters
3 centimeters

0.39 centimeters
0.39 centimeters

2.54 centimeters
2.54 centimeters

91.44 centimeters

Answer 3

To find the number of centimeters in 1 inch from the proportional relationship \(6y = 15.24x\), we can set \(x = 1\) (representing 1 inch) and solve for \(y\).

Starting with the equation:

\[ 6y = 15.24 \cdot 1 \]

This simplifies to:

\[ 6y = 15.24 \]

Next, we solve for \(y\):

\[ y = \frac{15.24}{6} \]

Calculating \(y\):

\[ y = 2.54 \]

Therefore, the number of centimeters in 1 inch is:

2.54 centimeters.