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proctortom

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Milk chocolate is being produced in a 300 litre tank, which initially contains 100 litres of milk. The following things then occur simultaneously:

1. Liquid cocoa (made up of equal parts cocoa solids and cocoa butter, both in liquid form) is added at a rate of 6 litres per minute.

2. Milk is added at a rate of 3 litres per minute. The well-stirred mixture leaves the tank via a tube, at a rate of 6 litres per minute.

The differential equation for dx/dt + 6x / (100 + 3t) = 3

......Therefore......

x(t) = (9t^3 + 900t^2 + 30,000t) / (3t + 100)^2

Find the time in minutes (t) for the mixture to be 25% Cocoa solids.