Question

Susie plans to run 2 miles per day the first week and then increase the daily distance by a half a mile each of the following weeks. How long before the marathon should she start?
There are many ways to approach this problem. Some include, make a table, write a function, create ordered pairs...

1. Identify and label the variables.
2.Make a table for up to 6 weeks to see a pattern.
3. Write an equation to represent the nth term of the sequence.
4. If the pattern continues during which week will she run 10 miles per day?
5. Is it reasonable to think that this pattern will continue indefinitely, explain?
6. How long before the marathon should she start?


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Answer 1

Due to length restrictions, we kindly invite to see the explanation below to know the answer with respect to each component of the question concerning linear equations.

How to determine a linear equation describing the daily distance of a runner

In this question we need to derive an expression of the daily distance as a function of time. Now we proceed to complete the components:

1. Linear equations have an independent variable (t - time) and a dependent variable (x - daily distance).
2. We notice that the daily distance increases linearly in time, then then we have the following pattern:
   
   t          1            2            3             4            5              6
   x          2          2.5          3           3.5           4             4.5
3. The equation that represents the n-th term of the sequence is x(n) = 2 + 0.5 · (n - 1).
4. The week when Susie will run 10 miles per day is:
   
   10 = 2 + 0.5 · (n - 1)
   8 = 0.5 · (n - 1)
   n - 1 = 16
   n = 17
   
   Susie will run 10 miles per day in the 17th week.
5. It is not reasonable to think that pattern will continue indefinitely as it is witnessed in the difficulties experimented by fastest runners in the world to increase their peak speeds.
6. A marathon has a distance of 26 miles, then we must solve the following equation:
   
   26 = 2 + 0.5 · (n - 1)
   24 = 0.5 · (n - 1)
   48 = n - 1
   n = 49
   
   Susie should start her training 49 weeks before the marathon.

To learn more on linear equation: brainly.com/question/11897796

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