(c) There are 500 students enrolled for MATH141 course in PMB and Howard college. A rumour starts to spread among these students that the next class test has been cancelled. Suppose that the rate at which this rumour spreads is proportional to the product of the fraction of the students in the course who have heard the rumour and the fraction of students in the course who have not yet heard it. At 8:00 am, 40 students have heard the rumour, and by 12:00 noon half the students have heard it. By what time would 90% of the students have heard the rumour?