(a) Jess runs on 5 days each week to prepare for a race. In week 1, every run is \(2\text{ km}\). In week 2, every run is \(2.5\text{ km}\). In week 3, every run is \(3\text{ km}\). Jess increases the distance of the run by \(0.5\text{ km}\) every week.

(i) Find the week in which Jess runs \(16\text{ km}\) on each of the 5 days.

(ii) Find the total distance Jess will have run by the end of week 8.

(b) Kyle also runs on 5 days each week to prepare for a race. In week 1, every run is \(2\text{ km}\). In week 2, every run is \(2.5\text{ km}\). In week 3, every run is \(3.125\text{ km}\). The distances he runs each week form a geometric progression.

(i) Find the common ratio of the geometric progression.

(ii) Find the first week in which Kyle will run more than \(16\text{ km}\) on each of the 5 days.

(iii) Find the total distance Kyle will have run by the end of week 8.