After knee surgery, the doctor tells Allen to return to his jogging program. The doctor suggests jogging for 15 minutes each day for the first week. Each week thereafter, the doctor suggests increasing the practice time by 5 minutes.

How many weeks will it take Allen to practice for 60 minutes?

a) 10 weeks
b) 8 weeks
c) 12 weeks
d) 9 weeks

To calculate the number of weeks Allen needs to jog for 60 minutes, you establish an arithmetic sequence starting with 15 minutes and a common difference of 5 minutes per week. The total time reaches 60 minutes after the 10th week.

Explanation:

The question requires a mathematical calculation to determine how many weeks it will take for Allen to build up his jogging time to 60 minutes. Allen starts with a jogging time of 15 minutes and increases his practice time by 5 minutes each following week. To calculate the number of weeks it will take for Allen to jog for 60 minutes, you can set up an arithmetic sequence starting at 15 minutes with a common difference of 5 minutes.

Since Allen is increasing his jogging time by 5 minutes each week, we can use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d, where an is the time he wants to achieve (60 minutes), a1 is the initial jogging time (15 minutes), n is the number of weeks, and d is the common difference (5 minutes).

60 = 15 + (n - 1)(5)

60 = 15 + 5n - 5

60 = 10 + 5n

50 = 5n

n = 10

Therefore, it will take Allen 10 weeks to build up to a jogging time of 60 minutes.