after a knee surgery your trainer tells you to return to your jogging program slowly suggest jogging for 12 minutes each day for the first week each week thereafter he just suggest that you have increased the time by 6 minutes per day on what week will it before you are up to jogging 60 minutes per day

To determine the week when you will be jogging 60 minutes per day, we can set up the following equation based on the given information:

- In the first week, you jog for 12 minutes per day.
- Each week, the jogging time increases by 6 minutes per day.
  
Let \( n \) represent the number of weeks, and we want to find \( n \) when the daily jogging time reaches 60 minutes.

### Expression for jogging time:

- In the first week: 12 minutes.
- In the second week: \( 12 + 6 = 18 \) minutes.
- In the third week: \( 18 + 6 = 24 \) minutes, and so on.

This forms an arithmetic sequence where:
- The first term \( a_1 = 12 \),
- The common difference \( d = 6 \).

The general formula for the \( n \)-th term of an arithmetic sequence is:

\[
a_n = a_1 + (n - 1) \cdot d
\]

Substituting the known values and setting \( a_n = 60 \) (the jogging time in the week we want to find):

\[
60 = 12 + (n - 1) \cdot 6
\]

### Solving for \( n \):

\[
60 = 12 + 6(n - 1)
\]
\[
60 - 12 = 6(n - 1)
\]
\[
48 = 6(n - 1)
\]
\[
n - 1 = \frac{48}{6} = 8
\]
\[
n = 8 + 1 = 9
\]

So, you will be jogging 60 minutes per day in the **9th week**.

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Do you want more details or have any questions?

Here are some related questions:
1. How would the result change if the daily time increased by 8 minutes instead of 6?
2. What if you started with 10 minutes in the first week instead of 12?
3. How many total minutes would you have jogged after 9 weeks?
4. How long would it take to reach 90 minutes per day if the increase remained 6 minutes per week?
5. What would the sequence look like if the increase was halved to 3 minutes per week?

**Tip**: Keep track of gradual progress in physical training to avoid injury and ensure long-term improvement!

After a knee surgery, your trainer tells you to return to your jogging program slowly, suggesting jogging for 12 minutes each day for the first week. Each week thereafter, he suggests that you increase the time by 6 minutes per day. On what week will it be before you are up to jogging 60 minutes per day?

Determine when you'll jog 60 minutes a day, starting at 12 minutes in the first week and increasing by 6 minutes weekly. This solution uses arithmetic sequences to find that it will take 9 weeks. Suitable for Grades 6-8 students learning about linear equations and sequences.

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