Question

You're planning the training program to run a marathon. You add 3.9 more miles to your program each week. In week four, you ran 20.6 miles. Write an equation that represents the distance you run in miles given a certain number of weeks.

Answer 1

To represent the distance you run in miles given a certain number of weeks, you can use the equation y = 8.9 + 3.9(x-1), where y is the distance and x is the number of weeks. The initial distance is found to be 8.9 miles.

Step-by-step explanation:

To write an equation that represents the distance you run in miles given a certain number of weeks, we can start by noting that in week four you ran 20.6 miles. We also know that you add 3.9 more miles to your program each week. So, we can represent the distance you run in week four as the initial distance plus 3.9 miles multiplied by the number of weeks minus one. Let's call the number of weeks 'x' and the distance you run 'y'.

In week four, you ran 20.6 miles. So, we have the equation: y = initial distance + 3.9(x-1)

To find the initial distance, we can substitute x = 4 into the equation and solve for y: 20.6 = initial distance + 3.9(4-1)

Now, we can simplify and solve for the initial distance:

20.6 = initial distance + 3.9(3)

20.6 = initial distance + 11.7

Subtract 11.7 from both sides:

8.9 = initial distance

So, the equation that represents the distance you run in miles given a certain number of weeks is y = 8.9 + 3.9(x-1). This equation will give you the distance you run based on the number of weeks.