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 and 16 minutes write an equation where why is the number of miles and ask is the time in minutes for the day you can run the fastest for the week
The equation representing this scenario can be written as:
M(x) = y
where,
M represents the number of miles run
x represents the day of the week (1 for Monday, 2 for Wednesday)
y represents the time taken in minutes for the run on that day
Now, let's input the given values into the equation:
M(1) = 4 miles in 40 minutes
M(2) = 2 miles in 16 minutes
The equation becomes:
M(1) = 4, y = 40
M(2) = 2, y = 16
Thus, the equation simplifies to:
y = 20x - 20
This equation represents the time in minutes for the day when you can run the fastest for the week.
To find the day of the week you can run the fastest, we need to compare the time it takes to run each day. We'll assign variables to represent the time and distance for each day.
Let's say:
- Monday: Distance = x miles and Time = y minutes.
- Wednesday: Distance = z miles and Time = w minutes.
From the given information, we know:
On Monday, x = 4 miles and y = 40 minutes.
On Wednesday, z = 2 miles and w = 16 minutes.
Since we want to find the day with the fastest time, we need to minimize the time variable. We can create an equation to compare the two times:
If y < w, then Monday is the fastest day.
If y > w, then Wednesday is the fastest day.
Comparing the times:
40 minutes < 16 minutes
So, the equation would be:
y < w
Plugging in the values we know, the equation becomes:
40 minutes < 16 minutes
Therefore, according to this equation, Wednesday is the day you can run the fastest for the week because it took you 16 minutes to run 2 miles.
To find the day when you can run the fastest for the week, we need to consider the time it takes for each run.
Let's define:
- x as the number of minutes it takes for Monday's run (4 miles in 40 minutes)
- y as the number of minutes it takes for Wednesday's run (2 miles in 16 minutes)
Since we want to find the day when you can run the fastest, we need to minimize the time. This means we need to find the smallest value between x and y.
To represent this mathematically, we can write the equation:
f(x, y) = min(x, y)
In this equation, f(x, y) represents the minimum value between x and y.
Now, we need to substitute the values of x and y into the equation.
For Monday's run, x = 40 minutes, so:
f(40, y) = min(40, y)
For Wednesday's run, y = 16 minutes, so:
f(x, 16) = min(x, 16)
These equations represent the time it takes for the fastest run in each respective day. To find the day when you can run the fastest for the week, you need to compare the values of f(40, y) and f(x, 16) and see which one is smaller.