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.
We need to find the day with the fastest running time. On Monday, you ran 4 miles in 40 minutes, which means a rate of 4 miles / 40 minutes = 0.1 miles per minute. On Wednesday, you ran 2 miles in 16 minutes, which means a rate of 2 miles / 16 minutes = 0.125 miles per minute. Since we're looking for the day with the fastest running time, we need to find the maximum rate.
Let's use y as the number of miles and x as the time in minutes for the day you ran the fastest. The rate for this day will be y/x miles per minute.
We have two rates: 0.1 miles per minute and 0.125 miles per minute. Since we're looking for the maximum rate, we can set up an equation:
y/x = max(0.1, 0.125)
Simplifying the equation, we find:
y/x = 0.125
Therefore, the equation is:
y = 0.125x
To write the equation, we need to compare the time it took to run 4 miles on Monday and the time it took to run 2 miles on Wednesday.
On Monday, you ran 4 miles in 40 minutes.
This can be expressed as: y = 4x / 40, where y represents the number of miles and x represents the time in minutes.
On Wednesday, you ran 2 miles in 16 minutes.
This can be expressed as: y = 2x / 16, where y represents the number of miles and x represents the time in minutes.
To find the day you ran the fastest for the week, you need to compare the two equations and determine when the values of y are equal.
To 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, we need to compare the two running sessions and determine which one had the fastest pace in terms of minutes per mile.
We can calculate the pace for each session by dividing the number of minutes by the number of miles. Then, we can compare the two pace values to find the session with the faster pace.
Let's start by calculating the pace for the first session on Monday:
Pace = Time / Distance = 40 minutes / 4 miles = 10 minutes per mile
Now let's calculate the pace for the second session on Wednesday:
Pace = Time / Distance = 16 minutes / 2 miles = 8 minutes per mile
Since 8 minutes per mile is faster than 10 minutes per mile, the second session on Wednesday is the one where you ran the fastest for the week.
Now, to write the equation where y is the number of miles and x is the time in minutes for the fastest running session, we have:
y = f(x)
Since we know the time for the fastest session is 16 minutes, we can substitute x = 16 into the equation:
y = f(16)
From the given information, we know that you ran 2 miles during the fastest session, so we can substitute y = 2 into the equation:
2 = f(16)
Therefore, the equation is 2 = f(16), where y is the number of miles and x is the time in minutes for the fastest running session.