The world record for the mile was 4:10 and 3:49 in 1975. Assuming that the record improves in a linear fashion (which it has so far) write an equation to predict the mile world record (in seconds) for a given year (y=record in seconds, x=year)

Question

The world record for the mile was 4:10 and 3:49 in 1975. Assuming that the record improves in a linear fashion (which it has so far) write an equation to predict the mile world record (in seconds) for a given year (y=record in seconds, x=year)

What should the world record be this year?

What should the world record be in 2001?

The world record was broken in 1993 by Noredine Morceli. What is the current world record in the mile? How does this compare to your prediction above?

Answer 1

"The fastest men's mile record is held by Hicham El Guerrouj of Morocco, who set the world mark at that distance with 3 minutes 43.13 seconds in Rome, Italy on July 7, 1999."

http://www.answerbag.com/q_view/6312

Answer 2

To write an equation to predict the mile world record for a given year, we need to use the concept of linear regression. Linear regression is a statistical method to describe a linear relationship between two variables. In this case, the variables are the year (x) and the record time in seconds (y).

Let's start by finding the slope of the linear regression line. To do this, we will calculate the change in record time divided by the change in years from 1975 to 1993:

Slope = (3:49 - 4:10) / (1993 - 1975)

Before proceeding, we need to convert the time to seconds. We'll use the format minutes:seconds. So, 3:49 will be 3 * 60 + 49 = 229 seconds, and 4:10 will be 4 * 60 + 10 = 250 seconds.

Slope = (229 - 250) / (1993 - 1975)
Slope = -21 / 18
Slope = -1.1667

Now that we know the slope, we can write the equation in the form of y = mx + b, where m represents the slope and b represents the y-intercept. We need to find the y-intercept (b) by substituting one known point into the equation. Let's use the point (1975, 250s).

250 = -1.1667 * 1975 + b
b = 250 + (1.1667 * 1975)
b = 250 + 2303.54
b = 2553.54

So, the equation to predict the mile world record (in seconds) for a given year is:

y = -1.1667x + 2553.54

Now, let's answer the questions:

1. To predict the world record for this year, substitute the current year as x into the equation:

y = -1.1667 * current_year + 2553.54

2. To predict the world record for 2001, substitute 2001 as x into the equation:

y = -1.1667 * 2001 + 2553.54

3. To find the current world record, we need to know the year it was broken or have more recent data.

The world record for the mile was 4:10 and 3:49 in 1975. Assuming that the record improves in a linear fashion (which it has so far) write an equation to predict the mile world record (in seconds) for a given year (y=record in seconds, x=year)

"The fastest men's mile record is held by Hicham El Guerrouj of Morocco, who set the world mark at that distance with 3 minutes 43.13 seconds in Rome, Italy on July 7, 1999."

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