Calculating Changing Distances: The Mystery of the Moving Innkeeper

In summary, the Mystery Machine is traveling at 55 mph and the innkeeper is standing 500 ft away from the highway. 1 minute later, the distance between them is increasing at a rate of 54.71 mph. This was determined using the formula 2x dx/dt + 2y dy/dt = 2z dz/dt, with dx/dt being 0 in this case.
  • #1
Differentiate
3
0
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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  • #2
Hi Differentiate! :smile:

What formula are you using? :confused:
 
  • #3
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.
 

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