Direct and Inverse Variation in One Problem
Date: 03/23/2006 at 15:44:58 From: Nicole Subject: Direct and Inverse Variation in one problem Dr. Math, I understand the difference between direct and inverse variation, but I'm having a hard time figuring out this problem that combines the two together: If s varies directly as r and inversely as t, and s = 10 when r = 5 and t = 3, for what value of t will s = 3 when r = 4? The answer in the back of the book is 8, but I can't figure out how to get that number! I'm not sure if you do it out as 2 separate problems and then combine them or if it should be one problem together. For Inverse: k = sr k = (10)(5) k = 50 For Direct: k = s/t k = 10/3 Then to combine them: 3 = (10/3)t Which is completely wrong! Thanks!
Date: 03/23/2006 at 16:15:42 From: Doctor Douglas Subject: Re: Direct and Inverse Variation in one problem Hi Nicole, Note that the problem stated that S varies directly as R and inversely as T (not the other way round as you seem to have worked out above). We can write two equations: s = b*r b is a constant that is independent of r, but not necessarily independent of t. s = c/t c is a constant that is independent of t, but not necessarily independent of r. Combining these two equations, we have s = k*r/t we can now see that everything works out (because s varies directly with r (with b = k/t), and inversely with t (with c = k*r). Now you can finish from here, right? - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/
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