Question

Part 2

To train for an upcoming marathon, Susie plans to run 2 miles per day the rst week and then increase the daily distance by a half a mile each
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...
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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?

Answer 1

To train for a marathon, Susie increments her daily running distance by half a mile each week. Using an arithmetic sequence formula, it's determined she'll reach 10 miles per day by week 17. However, the training pattern is not sustainable indefinitely due to physical limits and the need for recovery.

Step-by-step explanation:

Identifying Variables and Creating a Table

To approach the question of how Susie should train for her marathon, let us start by defining our variables and creating a table to visualize the progression of her running plan:

Let W represent the week number and D represent the distance run per day in miles.

Week 1: W=1, D=2 miles

Week 2: W=2, D=2.5 miles

Week 3: W=3, D=3 miles

Week 4: W=4, D=3.5 miles

Week 5: W=5, D=4 miles

Week 6: W=6, D=4.5 miles

Formulating an Equation

To represent the nth term of the sequence, we can use the arithmetic sequence formula:

D = 2 + (n - 1) * 0.5

Determining Week for 10 Miles Per Day

Using the derived equation, we can solve for n when D=10:

10 = 2 + (n - 1) * 0.5

n-1 = 16

n = 17

Susie will run 10 miles per day on the 17th week of her training.

Reasonableness of the Pattern

It is not reasonable to assume that this pattern will continue indefinitely because there are practical limits to the distance that can be run daily, and the body needs to rest and recover to prevent injuries.

Starting Time for the Marathon

The starting time for the marathon training would depend on several variables: Susie's current fitness level, the length of the marathon, and the maximum daily distance she aims to achieve before the event.