(i) The distances form a geometric sequence with the first term as x and a common ratio of 1.1. The distance on day 21 is given by:

\(x(1.1)^{20} = 20\)

Solving for \(x\):

\(x = \frac{20}{(1.1)^{20}} \approx 3.0\)

Thus, the distance on day 1 is 3.0 km.

(ii) The total distance run over 21 days is the sum of a geometric series:

\(S = x \frac{(1.1)^{21} - 1}{1.1 - 1}\)

Substituting \(x = 3.0\):

\(S = 3.0 \frac{(1.1)^{21} - 1}{0.1} \approx 192\)

Therefore, the total distance run over 21 days is 192 km.