Science:Math Exam Resources/Courses/MATH101/April 2011/Question 05 (a)

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MATH101 April 2011
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Question 05 (a)

Bird-Bath and Beyond Incorporated is famous for its Quetzal attracting bird-feeder solution made from water, honey and cane-sugar.

To make their solution, both honey and a cane-sugar solution are poured into a 200 L mixing tank. The honey is poured in at a rate of 1 L per minute while the sugar solution is poured in at 9 L per minute. Note that 1 L of honey contains 1 kg of sugar, while the cane-sugar solution contains 100g of sugar per L.

Unfortunately today there is a problem with the mixing tank. It was thoroughly cleaned and is initially filled with pure water, but main valve was broken and the water cannot be drained. When the mixing process is started, the honey and sugar-solutions are poured into the tank, and the excess fluid flows out of an emergency valve at 10 L per minute and onto the floor. You should assume that the solutions mix immediately and thoroughly in the tank.

(a) Give a differential equation that is satisfied by the amount of sugar in the tank after time t.

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