When Marcia started walking a 6 mile section of the trail, it took her 3.3 hours.After 1week her time was 3.1hours and after 2 weeks, it was 2.9 hours. If the pattern continues, what will Marcia's time be after 5 weeks?
3.3 - 5(.2) = ?
To determine Marcia's time after 5 weeks, we need to find the pattern in the time it takes her to walk the trail section. Let's analyze the given data:
- Marcia took 3.3 hours to walk the trail section when she started.
- After 1 week, her time decreased to 3.1 hours.
- After 2 weeks, her time further decreased to 2.9 hours.
As we can see, Marcia's time is gradually decreasing as she continues walking the trail section. To determine the pattern, we can calculate the rate at which her time is decreasing per week.
To calculate the rate, we can take the difference between the time after 1 week and the time after 2 weeks:
2.9 hours - 3.1 hours = -0.2 hours
We see that her time decreased by 0.2 hours within a one-week period. Therefore, we can assume that her time will continue to decrease at a rate of -0.2 hours per week.
Now, let's calculate her time after 5 weeks:
Time after 2 weeks: 2.9 hours
Rate of decrease: -0.2 hours per week
To calculate Marcia's time after 5 weeks, we can use the formula:
Time after n weeks = Time after 2 weeks + (Rate of decrease * (n - 2))
Substituting the values:
Time after 5 weeks = 2.9 hours + (-0.2 hours * (5 - 2))
= 2.9 hours + (-0.2 hours * 3)
= 2.9 hours + (-0.6 hours)
= 2.3 hours
Therefore, Marcia's time after 5 weeks will be approximately 2.3 hours.