Name: Rebecca Edwards
-Ok, I haven't got very far with this problem because its complicated. I know that I should start by finding differential equations, especially for the rate of change of the syrup, but I'm confused because its being added and subracted at the same time. I also know the volume stays constant, at 500 liters, because the total amount being added and subtracted are the same: 10 liters per minute. But the ratios are different and I don't know how to figure it out. Please help! Thank you!Hi Rebecca,
It helps here to think in terms of input and output. If the amount of syrup in the tank at time t is s(t) then
The syrup input rate you know, it is 2 liters/minute.
The liquid output rate is 10 liters/minute and the proportion of the liquid that is syrup is s(t)/500, hence the syrup output rate is s(t)/500 x 10 liters/minute. Thus
This is the differential equation you need to solve.Cheers,