I have a question for the masses. if you were traveling at 60 mph

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In summary, the OP is trying to find a way to calculate how long it will take to walk the equivalent distance to his house, based on his current speed. He arrives at an answer of 1 hour and 1760 yards, or 1 mile, at the last mile.
  • #1
trix5153
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I have a question for the masses.
if you were traveling at 60 mph and were 60 miles from your destination you would be 1 hour away from your point.

when you reached 59 miles away from your point you drop your speed to 59 mph. you are 1 hour away.

when your 1 mile from your point you drop your speed to 1 mile per hour. you are 1 hour away
... if you continue this for infinity you would always be 1 hour from your destination... I'm looking for some real help with this. is this correct?
 
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  • #2


similar to zeno's paradox?
 
  • #3


Ravalanche said:
similar to zeno's paradox?

No, this is NOT similar, really, to Zeno and the OP is correct that he would always be 1 hr from destination.
 
  • #4


phinds said:
...the OP is correct that he would always be 1 hr from destination.
No.

He can only claim to be "one hour away" from his destination under the proviso that he were to remain at the current speed for the rest of the journey.

He won't. It is not true that he is "an hour from his destination".

Yes, he is reducing his speed the closer he gets. He will never reach his destination. In fact, if we consider his change of rate of speed, we can confidently say "he is infinitely far (in duration) away from his destination" at all points.
 
  • #5


DaveC426913 said:
No.

He can only claim to be "one hour away" from his destination under the proviso that he were to remain at the current speed for the rest of the journey.

He won't. It is not true that he is "an hour from his destination".

Yes, he is reducing his speed the closer he gets. He will never reach his destination. In fact, if we consider his change of rate of speed, we can confidently say "he is infinitely far (in duration) away from his destination" at all points.

DOH you're right, obviously
 
  • #6


Thank you all for your posts. I'm sorry for my ignorance, I thought of this when i was 16 and have never asked the question to some "SMART" people before. Is there a name for this? or is it just a know point in the community that this is true? Thanks again.
 
  • #7


trix5153 said:
Thank you all for your posts. I'm sorry for my ignorance,..

Never apologize for not knowing something or for asking. A curious mind is a most treasured thing, especially around here.

trix5153 said:
Is there a name for this?

It is a convergent series.

An infinite series of numbers can add up to a finite number.

1/2 + 1/4 + 1/8 + 1/16 + 1/32 +1/64 + ... = 1
 
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  • #8


Actually, since he's changing his speed in 1mph steps, he will get there unless he changes his formulation...

He's approximating a hyperbolic approach, but only approximating.
 
  • #9


Sorry you will never arrive at your destination.

Figure out how far you go in each 1 min interval, sum them up. You will have traveled 30.5 miles when your speed reachs 0.
 
  • #10


As the question is posed he does reach his destination, because the speed change only occurs at the mile markers. So at the last mile, 1 mile from home he slows to 1mile and hour. An hour later he arrives at his destination and changes his speed to 0mph.
 
  • #11


tony_physic said:
As the question is posed he does reach his destination, because the speed change only occurs at the mile markers. So at the last mile, 1 mile from home he slows to 1mile and hour. An hour later he arrives at his destination and changes his speed to 0mph.
This sounds right to me. At each mile marker he's dropping his speed by 1 mph.

What that means is only that each mile takes progressively more time to cover, with the last mile taking a full hour.

Is there a quick way to add up the times and find out how long the trip takes doing it this way? I'm curious.

Working backward:

Mile 60 = 1 hr
Mile 59 = 1/2 hr
Mile 58 = 1/3 hr
Mile 57 = 1/4 hr
Mile 56 = 1/5 hr
Mile 55 = 1/6 hr
Mile 54 = 1/7 hr &etc

It's clear the bulk of the added time comes at the end of the trip and does not threaten to approach an infinite amount of time, or anything like that. Still, I'd expect the total time it takes to do it this way to be interesting in some way, shape, or form.
 
  • #12


You are all wrong in your reasoning, a human is not some infinitely small point, he/she occupies a definite volume and space. Take it from the last mile, or 1760 yds, which is covered in 1 hour. Then going on decreasing the distance the time increases , 2 hrs for the half mile, 4 hours for the quarter mile and so on. Until finally when he reaches the last yard (0.8593 yds to be exact) he takes 2048 hours or 85.3 days to cross that small distance. The point being that he does make it, even if it takes a long time!
 
  • #13


zoobyshoe said:
Is there a quick way to add up the times and find out how long the trip takes doing it this way? I'm curious.
I've got about 4.68 hours. Wolfram Alpha can do it in no time.
 
  • #14


nasu said:
I've got about 4.68 hours. Wolfram Alpha can do it in no time.
Thanks, nasu!

Well, that figure isn't as interesting as I'd hoped it would be.
 
  • #15


I have the answer for you. It is not a black or white answer and will surely piss off all those who like simple answers.

For the same reason that Schrödinger's cat is both dead and alive - a very real consideration in quantum physics, in your puzzle, the answer is that you will arrive at the destination eventually; however, it will take forever.
 
  • #16


McQueen said:
You are all wrong in your reasoning, a human is not some infinitely small point, he/she occupies a definite volume and space. Take it from the last mile, or 1760 yds, which is covered in 1 hour. Then going on decreasing the distance the time increases , 2 hrs for the half mile, 4 hours for the quarter mile and so on. Until finally when he reaches the last yard (0.8593 yds to be exact) he takes 2048 hours or 85.3 days to cross that small distance. The point being that he does make it, even if it takes a long time!
Why did you stop at one yard? Why do you all along assume he's halving the distance and halving the speed, and then when it gets down to a yard, you declare he just magically leaps across that distance?

As for a human being a non-zero size, this is not relevant unless you get sloppy with your measurements. When he started his journey, his toe (or bumper) had not crossed the starting line, and he's not done until that toe (or bumper) crosses the finish line. This is true whether he is a point, a person, a car or a whale. The point of measurement is indeed a zero-dimensional point.

Talk about being "wrong in reasoning". You did it twice in one paragraph. :biggrin:
 
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  • #17


It is up to the Engineers amongst us to say those immortal words "Near enough for Jazz". If you can't measure the separation distance then you've arrived.
 
  • #18


sophiecentaur said:
It is up to the Engineers amongst us to say those immortal words "Near enough for Jazz". If you can't measure the separation distance then you've arrived.

Agreed. If this were an Engineering Forum. But it ain't. :biggrin: We eat zero-dimensional points for breakfast.
 
  • #19


DaveC426913 said:
Agreed. If this were an Engineering Forum. But it ain't. :biggrin: We eat zero-dimensional points for breakfast.

Indigestion for the rest of the day?
:wink:
 
  • #20


Eventually the object would come to a movement so slow it wouldn't even matter.
 
  • #21


16 years old said:
...it wouldn't even matter.
A physicist will look at you like to just sprouted antennae.


Imagine a physicist saying...

"Well, we use a microscope to look at smaller and smaller things until we get down to these atom-thingies. That's small enough. Anything smaller doesn't really matter does it?"

:biggrin:
 

1. How long would it take to travel 60 miles at 60 mph?

If you were traveling at a constant speed of 60 mph, it would take you exactly 1 hour to travel 60 miles. This is because the equation for calculating time is distance divided by speed, so 60 miles divided by 60 mph equals 1 hour.

2. Can you travel 60 miles in one hour at a speed other than 60 mph?

Yes, you can travel 60 miles in one hour at a speed other than 60 mph. The key factor is the distance traveled, so as long as you cover a distance of 60 miles in one hour, your speed can vary. For example, you could travel 120 mph and cover 60 miles in 30 minutes.

3. What is the distance traveled after 30 minutes at 60 mph?

After 30 minutes of traveling at 60 mph, you would have covered a distance of 30 miles. This can be calculated by multiplying 30 minutes (0.5 hours) by 60 mph, resulting in 30 miles.

4. How does traveling at 60 mph compare to other speeds?

Traveling at 60 mph is considered a moderate speed compared to other modes of transportation. For example, the average speed of a car on the highway is around 65 mph, while a commercial airplane can travel at speeds of over 500 mph.

5. What are some factors that can affect travel time at 60 mph?

Some factors that can affect travel time at 60 mph include traffic, road conditions, and weather. If there is heavy traffic or poor road conditions, it may take longer to cover a distance of 60 miles at 60 mph. Additionally, strong headwinds or inclement weather can also impact travel time.

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