Problem solving about differential equation

The organiser of sale, which lasted for 3 hours and raised a total £1000, attempted to create a model to represent the relationship between s and t, where £ s is the amount which had been raised at time t hours after the start of the sale. In the model s and t were taken to be continous variables. The organiser assumed that rate of raising money varied directly as the time remaining and inversely as the amount already raised.  

a.     Find the equation of s in terms of t

b.     Find the amount raised during the first hour of sale

c.      Find the rate of raising money one hour after the start of the sale

Solution

First we must make a model for this problem.

The organiser of sale assumed that the rate of raising money raised varied directly as the time remaining which is (3 – t)  and inversely as the amount already raised (s)

Where k is a constant

We arrange the equation