How should I aproach a connected rates of change question.
You should start by identifying which parts have a fixed rate of change e.g. water is being poured in at 50 cm^3/s. You should then identify what is changing in relation to this e.g the height of fluid in a container. you will often be given a formula that relates these things such as volume to height or in the case of a standard shape like a pyramid you might be expected to know it. You then find what the new relation they want is e.g. height of water with respect to time, and construct this by treating the 2 differential equations you already have as fractions and multiply the together to creat the desired relation.
KC
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C4 June 2014 Q4: Water is flowing into a vase. When the depth of water is h cm, the volume of water V cm^3 is given by V=4πh(h+4). Water flows into the vase at a constant rate of 80π cm^3/s. Find the rate of change of the depth of water in cm/s, when h=6.