A rumor spreads through a school. Let $y(t)$ be the fraction of the population that has heard the rumor at time $t$ and assume that the rate at which the rumor spreads is proportional to the product of the fraction $y$ of the population that has heard the rumor and the fraction $1-y$ that has not yet heard the rumor.

The school has 1000 students in total. At 8 a.m., 94 students have heard the rumor, and by noon, half the school has heard it. Using the logistic model explained above, determine how much time passes before 90% of the students will have heard the rumor.

90% of the students have heard the rumor after about hours.