When were the boats closest to each other?

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SUMMARY

The discussion revolves around determining the point in time when two boats are closest to each other. One boat departs from a dock at noon traveling west at 25 km/h, while the second boat heads north at 20 km/h and arrives at the dock at 1:00 PM. The key to solving the problem lies in applying the Pythagorean theorem to calculate the distance between the two boats over time. The participants emphasize the importance of correctly setting up the equations to find the minimum distance.

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  • Pythagorean theorem application
  • Understanding of relative motion
  • Basic algebra for solving equations
  • Knowledge of speed, distance, and time relationships
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  • Learn about relative velocity and its impact on distance calculations
  • Explore optimization techniques in calculus for minimizing distances
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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:
 

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