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Topic: Easy: Hummingbird (Read 9258 times) |
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ootte
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Easy: Hummingbird
« on: Jul 24th, 2002, 2:16am » |
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The trains move towards each other at a speed of 35 mph. 5000 miles will be done in 142.86h then. After 142.86h the train from LA travelled 2142.9 miles and the train from NY travelled 2857.2 miles. In 142.86h the hummingbird flew 142.86 h * 25 mph = 3571.5 miles. It doesn't matter that the hummingbird flies back and forth, it's only the time that matters.
Comments are appreciated.
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Oliver
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edyforfun
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Re: Easy: Hummingbird
« Reply #1 on: Jul 27th, 2002, 10:31am » |
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I came out with the same answer too. The two trains must have travelled for the same time period to collide, and since both trains travelled at different speed, the distance each train have travelled can be different. However, the addition of the distances both trains have travelled must be 5000 miles.
x = time required for the 2 trains to collide.
15x + 20x = 5000
35x = 5000
x = 5000/35 = 142.86 hours
Thus, the hummingbird has travelled 142.86 x 25 = 3571.5
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rfeague
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Re: Easy: Hummingbird
« Reply #2 on: Sep 7th, 2002, 12:33pm » |
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What's really great about this puzzle is you can solve it the easy way (the way you guys did) or you can solve it the hard way (the way C. Clark did in the thread "Here are the easy answers"). It seems very hard if you try to add up the number of oscillations back and forth the bird made.
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explosion
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Re: Easy: Hummingbird
« Reply #3 on: Dec 3rd, 2002, 2:00pm » |
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Haven't you thought that railway between New York and Los Angeles is NOT straight?
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Icarus
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Re: Easy: Hummingbird
« Reply #4 on: Dec 3rd, 2002, 7:04pm » |
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on Dec 3rd, 2002, 2:00pm, explosion wrote:| Haven't you thought that railway between New York and Los Angeles is NOT straight? |
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The answer still holds, as long as 5000 miles is the length of the railway, not the straight line length. And it does not matter what route the hummingbird takes between the two trains. The total distance it flies remains the same, because the answer depends only on its speed and flight time.
Note that the "hard" way of doing this becomes impossible if the hummingbird does not follow the track, but the "easy" answer is unchanged.
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A Hidden Cow
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Knitpicking, but the riddle implys, but doesn't specifically <i>say</i> that the two trains leave their respective cities at the same time.
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A Hidden Cow
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Oops! Heh, just thought I could throw HTML in there, I guess not, I also misspelled "implys". Oh well...
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william wu
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Re: Easy: Hummingbird
« Reply #7 on: Dec 15th, 2002, 12:02am » |
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To: A Hidden Cow
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logan
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Re: Easy: Hummingbird
« Reply #8 on: Nov 28th, 2006, 2:42am » |
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i didn't make the calculations but in terms of math perivious calculations looks right. But something about physics disturbed me. When two trains are rushing each other as the distance close up humming bird will make quick come and goes between trains. This quick flights will get narrower and narrower until the impact.
The deal is that you cannot calculate an accurate distance since for the right measurements even the centimeters and milimeters before crush humming bird is still flying (also moment of crush.. what is the "moment" in terms of physics?). thus result will end like number X,abcd.... where after comma goes to infinity. Thus it is noy quite possible to reach to an exact statement.
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| « Last Edit: Nov 28th, 2006, 3:11pm by Icarus » |
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towr
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Re:
« Reply #9 on: Nov 28th, 2006, 2:58am » |
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on Nov 28th, 2006, 2:42am, logan wrote:| thus result will end like number X,abcd.... where after comma goes to infinity. Thus it is noy quite possible to reach to an exact statement. |
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That doesn't mean much. 0.999...=1 and a number like sqrt(2) also goes on with infinite decimals.
And in fact, in this case there is an exact number, if we abstract the hummingbrid to a point (as is customary in maths and physics)
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Icarus
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Re: Easy: Hummingbird
« Reply #10 on: Nov 28th, 2006, 3:29pm » |
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Any time you apply mathematics to a real world situation, you make approximations. Measurements in the real world come with uncertainty - and this is not just because of limits on our ability to measure, but because the quantity we are measuring is itself not defined past a certain accuracy.
For example, if you are given a rod and asked to measure exactly how long it is, you could quickly give the answer "1 meter", but this is only a general answer. If you needed the length to a millimeter or less, then you first have to ask: at what temperature am I measuring? For, while the length of the bar without regard to temperature is well-enough defined for meter-accuracy, it is not well-enough defined for millimeter accuracy.
By fixing the temperature and pressure at which the bar is to be measured, you can obtain an accuracy to micron level. But at the angstrom level, the length is not well-defined again, as you must now define what mathematical surface about the atoms of the rod constitute its limits. Once you have accomplished that, you next run into the limitations of the definition of "meter" (though unless you have some revolutionary new means of measurement, you will run into the limitations of your equipment either before or at the same time as this).
It is to be understood that any time we apply mathematics to the real world, we are only approximating the fuzzy real world situation with our infinitely precise mathematical model.
But the fact is, this is not a physical puzzle, but a mathematical one. One clear indicator of this is the fact that the bird is already acting in a physically impossible manner long before the trains approach each other (the infinitely fast direction changes when it reaches each train).
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sks2141
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Re: Easy: Hummingbird
« Reply #11 on: Jan 23rd, 2007, 5:30am » |
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How can be the same problem be approached if the distance between LA n NY is not know beforehand:
Is it possible to use substitution and elimination methods for deriving the final answer or the final answer will be in terms of some constant only ? 
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Icarus
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Re: Easy: Hummingbird
« Reply #12 on: Jan 23rd, 2007, 4:59pm » |
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There is not enough information in the riddle to deduce the distance if it were not given. Therefore there cannot be enough information to deduce the time either.
If you were not given the distance, the best you could answer is that the hummingbird travels (5/7)D, where D is the length of the train track connecting the two cities.
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samspade1945
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Re: Easy: Hummingbird
« Reply #13 on: Jun 30th, 2009, 4:45am » |
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Hi, my algebra skills seem to be a bit rusty, I originally came up with this,
[(x mi / 15 mph) - (x mi / 20 mph)] = T hours, the amount of time until the trains crash.
T hours * 25 mph = D miles, the distance the bird can travel before the trains crash.
Combining:
[(x mi / 15 mph) - (x mi / 20 mph)] * 25 mph = D miles
[(4x mi / 60 mph) - (3x mi / 60 mph)] * 25 mph = D miles
(x mi / 60 mph) * 25 mph = D miles
25x mi / 60 = D miles
5x mi / 12 = D miles
(5 * 5000) mi / 12 = 2083.333... miles
And I am wondering why
[(x mi / 15 mph) - (x mi / 20 mph)] = T hours, the amount of time until the trains crash.
doesn't give the correct time for impact. I've figured out that it gives the difference in time between when the second train arrives in LA and the first train arrives in New York if they were on parallel tracks, but why isn't also the time until the collison?
Can someone please help?
thank you
-edit
I understand now, thank you for your help towr
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| « Last Edit: Jun 30th, 2009, 10:03pm by samspade1945 » |
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towr
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Re: Easy: Hummingbird
« Reply #14 on: Jun 30th, 2009, 5:27am » |
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on Jun 30th, 2009, 4:45am, samspade1945 wrote:And I am wondering why
[(x mi / 15 mph) - (x mi / 20 mph)] = T hours, the amount of time until the trains crash.
doesn't give the correct time for impact. I've figured out that it gives the difference in time between when the second train arrives in LA and the first train arrives in New York if they were on parallel tracks, but why isn't also the time until the collison? |
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Because the distance between the trains decreases by 15+20=35 mph.
Suppose both trains go 20 mph, would you say they should immediately crash, just because they would have arrived at their destination at the same time if they were on parallel tracks?
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