(i) The time taken for each mile forms an arithmetic sequence where the first term is 5 minutes (or 300 seconds) and the common difference is 12 seconds. The nth term of an arithmetic sequence is given by:

\(a_n = a + (n-1) imes d\)

where \(a = 300\) and \(d = 12\). We need to find \(n\) such that \(a_n = 540\) (since 9 minutes is 540 seconds):

\(540 = 300 + (n-1) imes 12\)

\(240 = (n-1) imes 12\)

\(n-1 = 20\)

\(n = 21\)

(ii) The total time for 26 miles is the sum of the arithmetic sequence with 26 terms. The sum \(S_n\) of an arithmetic sequence is given by:

\(S_n = rac{n}{2} imes (2a + (n-1) imes d)\)

For \(n = 26\), \(a = 300\), and \(d = 12\):

\(S_{26} = rac{26}{2} imes (2 imes 300 + 25 imes 12)\)

\(S_{26} = 13 imes (600 + 300)\)

\(S_{26} = 13 imes 900 = 11700\) seconds

Convert 11700 seconds to hours and minutes:

\(11700 ext{ seconds} = 3 ext{ hours and } 15 ext{ minutes}\)