A school is organizing a Mega Science Exhibition where student teams are demonstrating live experiements. To manage the event, the coordinators track the participant counts and recurring presentation scehdules for three major exhibition zones.
Robotics Zone -\(90\) participants (Presentation loop repeats every \(15\) minutes)
Space Exploration Zone -\(135\) participants (Presentation loop repats every \(20\) minutes)
Chemistry Zone -\(180\) participants (Presentation loop repeats every \(30\) minutes)
(i) Before the main event, all participants must attend a breifing session. If each briefing room must accommodate the same number of participants and participants from different zones cannot be seated in the same room.
What is the maximum number of particpants that can be accomodated in each room?
(ii) What is the minimum number of rooms required during the event?
(iii) What is the simplest ratio of the minimum number of briefing rooms required for Robotics , Space science and Chemistry zones?
(iv) If all three exihibition zones begin their very first presentation loop simultaneoulsy at \(10.00\) AM, at what time all three zones start their presentations together again?