Question

You are training twice a week for a race. On monday, you go 4 miles in 40 minutes. then on wednesday you go 2 miles in 16 minutes. write an equation where y is the number of miles and x is the time in minutes for the day you ran the fastest for the week.

Answer 1

Let's assume that the equation represents a line, where y represents the number of miles and x represents the time in minutes. The equation for this line can be written in the form:

y = mx + b

To find the equation, we need to determine the slope (m) and the y-intercept (b) of the line.

First, let's determine the rate of speed for each run:

For Monday:
Distance (y1) = 4 miles
Time (x1) = 40 minutes
Rate of Speed (m1) = y1/x1 = 4/40 = 1/10 mile per minute

For Wednesday:
Distance (y2) = 2 miles
Time (x2) = 16 minutes
Rate of Speed (m2) = y2/x2 = 2/16 = 1/8 mile per minute

Since we are looking for the day you ran the fastest, we need to find the higher rate of speed. Let's compare the values:

m1 = 1/10 mile per minute
m2 = 1/8 mile per minute

The higher rate of speed is 1/8 mile per minute from Wednesday's run, so we will use m = 1/8.

Now let's find the y-intercept (b). We can use the point-slope form of the equation:

y - y1 = m(x - x1)

Using the coordinates from Wednesday's run (2, 16):

y - 2 = (1/8)(x - 16)
y - 2 = (1/8)x - 2
y = (1/8)x

Thus, the equation representing the day you ran the fastest is:

y = (1/8)x