[Uni Differential Equations] Solving for time HomeworkHelp

So Jim works at a restaurant and wants to put soup in the refrigerator at the end of the day. Only problem is that the soup is too hot to be put directly into the sink. Jim cools the soup by placing the container of soup in a sink with running water.

I need to solve for how long he should make the soup in advance for it to cool down to the appropriate temperature.

I'm given the simmering temperature of the soup (95 C), temp at which water can be put into the fridge (8 C), the temperature of the water used to cool down the soup (8 C), the temp of the water after m minute in the water at temperature W (45 C) and the number of minutes the pot stays in the water at temperature W (8 minutes).

I'm pretty sure this falling into a first order autonomous DE. Which means I'd use the equation y=(b/a)+Ce^at to get a relation involving time. However in order to get my first DE ((dy/dt)=ay-b) I need to know the rate at which the soup cools. Do I use the fact that the water starts at 95 C, then after 8 minutes its at 45 c?

So the rate is 50 C/ 8 min?

Submitted February 02, 2016 at 01:22AM by Im_an_Owl http://ift.tt/1SofhIp HomeworkHelp