Question

After an injury, Greg's doctor advises him to slowly build up to his regular workout schedule, adding a certain number of minutes to his workout time each week. According to his doctor's advice, Greg should work out for 25 minutes in week 3 and 47.5 minutes in week 6. A. For how many minutes should Greg work out in week1? In week 10? Show your work.

Answer 1

To determine the workout times for Greg in week 1 and week 10, we calculate the weekly increment from the provided times for week 3 and week 6, resulting in Greg working out for 10 minutes in week 1 and 77.5 minutes in week 10.

Step-by-step explanation:

To calculate the minutes Greg should work out in week 1 and week 10, we need to determine the rate at which the workout time increases each week. We know Greg works out for 25 minutes in week 3 and 47.5 minutes in week 6.

1. First, find the difference in workout times between week 3 and week 6:
   47.5 minutes (week 6) - 25 minutes (week 3) = 22.5 minutes.
2. The increase occurs over 3 weeks (from week 3 to week 6), so we divide the total increase by the number of weeks to find the weekly increase:
   22.5 minutes ÷ 3 weeks = 7.5 minutes per week.
3. To find the workout time for week 1, we subtract the weekly increase twice from the workout time in week 3:
   25 minutes - 7.5 minutes - 7.5 minutes = 10 minutes.
4. To find the workout time for week 10, add the weekly increase four times to the workout time in week 6:
   47.5 minutes + 7.5 minutes × 4 weeks = 77.5 minutes.

Therefore, Greg should work out for 10 minutes in week 1 and 77.5 minutes in week 10.