In a community of 800 people the rate at which a rumor spreads is jointly proportional to the number of people who have heard the rumor and the number of people who have not heard it. Given that the rumor is spreading at the rate of 20 people per hour when 200 people have heard it, how fast is the rumor spreading when 500 people have heard it?

Question

In a community of 800 people the rate at which a rumor spreads is jointly proportional to the number of people who have heard the rumor  and the number of people who have not heard it. Given that the rumor  is spreading at the rate of 20 people per hour when 200 people have heard it, how fast is the rumor spreading when 500 people have heard it?

Steve · Answer

If x have heard and y have not, and if r is the spread rate, r = kxy That is, r/(xy) = k is constant. So, you want r such that r/(500*300) = 20/(200*600)