Minimizing the Time to Rescue
Date: 11/29/1999 at 20:21:30 From: Chris Palmquist Subject: Calculus (A related rate and optimization problem) I'm standing on the beach at a certain point - let's call this point (0,0). There is a man drowning in the water 300 meters down the beach and 100 meters out. Call his point (300, 100). I can run 5 meters per second and can swim 3 meters per second. How far should I run along the beach before jumping in the water and swimming to the drowning man in the fastest time? I've tried everything on this problem and I just can't get it. I know you need to use the related rate to find the minimum, but I can't really get started on this question. Please help me out.
Date: 11/30/1999 at 08:13:54 From: Doctor Jerry Subject: Re: Calculus (A related rate and optimization problem) Hi Chris, Let the beach be the x-axis with your present position the origin. You want a point x, 0 <= x <= 300, for which the sum of TW+TS is a minimum, where TW is the time walking from (0,0) to (x,0) and TS is the time spend swimming from (x,0) to (300,100). Each is a constant rate situation and so D = R*T, or T = D/R. I hope that will get you started. I think it's a mistake to try to over-categorize a problem before dealing with it directly. I'm referring to your feeling that it is a related rates problem. - Doctor Jerry, The Math Forum http://mathforum.org/dr.math/
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