When were the boats closest to each other?

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Homework Statement


A boat leave a dock at noon and heads weat at a speed 25km/h. Another boat heads north at 20km/h and reaches the same dock at 1:00 pm. when were the boats closest to each other?


Homework Equations


when were the boats closest to each other?



The Attempt at a Solution


I use the pythagorean for the distance
but I'm not sure about how to sub them in?
I tried to assume that the second boat also leaves at noon, so the total distance will be 20km. But that's wrong. Please help, thanks =P
 
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First, I think you have to find the rate of change of the hypotenuse.
 
Hi zapped! :smile:
zapped said:
A boat leave a dock at noon and heads weat at a speed 25km/h. Another boat heads north at 20km/h and reaches the same dock at 1:00 pm. when were the boats closest to each other?

I use the pythagorean for the distance
but I'm not sure about how to sub them in?
I tried to assume that the second boat also leaves at noon, so the total distance will be 20km. But that's wrong.

No, that assumption is fine (not necessary, but fine).

Anyway, minimising the pythagorean, which is what you tried to do, should have worked …

show us what you got for the pythagorean :smile:
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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