STPM2008数学题

MK705

这是一道去年STPM的一道数学题。。。我想了很久但还是无法解答。请你们帮帮我。
问题如下：
A 50 litre tank is initially filled with 10 litres pf brine solution containing 20 kg of salt. Starting from time t=0, distilled water is poured into the tank at a constant rate of 4 litres per minute. At the same time, the mixture leaves the tank at a constant rate of k^(1/2) litre per minute, where k^(1/2) >0. The time taken for overflow to occur is 20 minutes.

(a) Let Q be the amount of salt in the tank at time t minutes. Show that the rate of change of Q is given by:


dQ/dt= (-Qk^(1/2))/(10+(4-k^(1/2))t)


* k^(1/2) means square root of k,

Hence, express Q in term of t,

(b) Show that k = 4, and calculate the amount of salt in the tank at the instant outflow occurs.

(c) Sketch the graph of Q against t for 0 < t < 20

谢谢。。。。