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.
To determine how many miles John runs per hour, we need to solve the equation 4y = 26.2x.
The equation represents a proportional relationship between the time (x) and the distance (y). In this case, the time (x) is measured in hours, and the distance (y) is measured in miles.
To find the number of miles John runs per hour, we can rearrange the equation to solve for y.
Divide both sides of the equation by 4:
4y/4 = 26.2x/4
Simplifying gives us:
y = 6.55x
Now, we can see that the equation y = 6.55x represents a line with a slope of 6.55. This means that for every hour John runs, he covers a distance of 6.55 miles.
Therefore, John runs 6.55 miles per hour in the marathon.
To determine how many miles John runs per hour, we need to find the value of x in the equation 4y=26.2x when y=1 (since we want to find the number of miles he runs per hour).
Plugging in y=1, we have:
4(1) = 26.2x
4 = 26.2x
To isolate x, divide both sides of the equation by 26.2:
4/26.2 = x/1
0.15267176 = x
So, John runs approximately 0.1527 miles per hour.