Calculating Changing Distances: The Mystery of the Moving Innkeeper

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SUMMARY

The discussion centers on calculating the rate of change of distance between a moving object, the Mystery Machine traveling at 55 mph, and a stationary innkeeper located 500 feet from the highway. The correct rate of increase in distance after one minute is determined to be 54.71 mph. A participant initially miscalculated the rate due to an incorrect application of the differentiation formula but corrected it by setting the appropriate derivative to zero. The final answer aligns with the established mathematical principles of related rates in calculus.

PREREQUISITES
  • Understanding of calculus, specifically related rates
  • Familiarity with differentiation techniques
  • Knowledge of converting units (feet to miles)
  • Ability to apply the Pythagorean theorem in dynamic scenarios
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  • Study the concept of related rates in calculus
  • Learn how to apply the Pythagorean theorem in motion problems
  • Practice unit conversion techniques for speed and distance
  • Explore differentiation of functions involving multiple variables
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Students of calculus, educators teaching related rates, and anyone interested in applying mathematical principles to real-world motion problems.

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The Mystery Machine travels 55 mph down the highway of life. An innkeeper is standing 500 ft from the highway. How fast is the distance between the innkeeper and the Mystery Machine increasing 1 min later?

The answer says it is 54.71 mph.

I got something a bit more than 60 for the mph.
http://www.wolframalpha.com/input/?...*(55/60))/(2sqrt((500/5280)^2+(55/60)^2)))*60

I converted everything into miles and miles per min. So I got dy/dt=55/60. 1 min later, y=55/60. x=500ft=500/5280 miles.
 
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Hi Differentiate! :smile:

What formula are you using? :confused:
 
With that question I got the answer to this.
Thanks LOL.
I was using 2x dx/dt + 2y dy/dt = 2z dz/dt

I accidentally put dx/dt as a non zero when it is 0. When I made it 0, I got the right answer XD.