Hi, I'm looking at the ladder problem in the recitation session for lesson 31, related to rates of change. I can understand the solution being presented and I can't find any flaw with it. However I have what I believe is a simpler solution. The problem is the solution I come up with is different and I can't see the flaw of my solution either. My solution calls x to the base of the bigger triangle, y to its height. By Pithagorean Theorem and deriving we get to y' = - xx' / y (with ' notation meaning d/dt). At t=0, using triangle geometry you get x = 12 and y = 16. So it follows y'= -15/4.

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To follow up, what is wrong with my solution if anything :-)?

The rate of change dx/dt = 5 is the rate at which the distance between the base of the ladder and the wall changes. This is not the same as the rate at which the horizontal distance between the base and the top of the ladder (the base of the bigger triangle) changes. In your solution you assume it is and that's where your problem lies.

Matt, thanks very much for your answer. What you say makes sense and I was suspecting something like that. The problem I find is that it is very difficult to see it and I might do it wrong in a different context in the future. A bit of a rethorical question but any advice? :)

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