A rumor spreads at a rate proportional to the product of the fraction of the pop

Question

A rumor spreads at a rate proportional to the product of the fraction of the population who have heard the rumor and the fraction of the population who have not heard the rumor.  Suppose that 1,000 students are living in Joe West Hall, and that, at 8:00am, a small group of ten students hears that they will be serving meatloaf for dinner.  By noon, 400 students have heard the rumor.  How many of the students will have heard the rumor by the time the cafeteria opens at 5:00pm?
A rumor spreads at a rate proportional to the product of the fraction of the population who have heard the rumor and the fraction of the population who have not heard the rumor.  Suppose that 1,000 students are living in Joe West Hall, and that, at 8:00am, a small group of ten students hears that they will be serving meatloaf for dinner.  By noon, 400 students have heard the rumor.  How many of the students will have heard the rumor by the time the cafeteria opens at 5:00pm?

Explanation / Answer

Total = 1000 students

at noon i.e 12p.m. time taken = 12-8 = 4hrs

Fraction of people heard rumour = 10/1000

Unheard = 990/1000

Therefore 400 = cons * 10/1000 * 990/1000 * 4hrs

cons = (400*1000*1000)/(10 * 990 * 4)   = 1000000/99

Therefore by 5 pm time spent = 9hrs

Heard = cons * 10/1000 * 990/1000 * 9

           = 10 * 990 * 9 /99   = 900people

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.