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Topic: Racetrack Hint and Answer (Read 2583 times) |
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otter
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Racetrack Hint and Answer
« on: Aug 8th, 2002, 8:31am » |
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> You are at a track day at your local racecourse in your new Porsche. Because it's a crowded
> day at the track, you are only allowed to do two laps. You haven't driven your car at the track
> yet, so you took the first lap easy, at 30 miles per hour. But you do want to see what your
> ridiculous sports car can do. How fast do you have to go on the second lap to end the day
> with an average speed of 60 miles per hour?
HINT: How long does it take to complete the first lap?
ANSWER (hidden):
You cannot average 60 mph for both laps.
Let us assume a racetrack of x miles. For the first lap at 30 mph you complete the lap in 2x minutes.
To average 60 mph for both laps (2x miles) it would take 2x minutes, which you have already used up in your 30 mph lap. So you cannot average 60 mph for BOTH laps.
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Otter
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| « Last Edit: Oct 23rd, 2003, 8:09pm by Icarus » |
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We shall not cease from exploration. And the end of all our exploring will be to arrive where we started
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Geremy
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Re: Racetrack Hint and Answer
« Reply #1 on: Aug 15th, 2002, 6:41am » |
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Doesn't the Person have to travel Infinitely fast on the second lab to keep his average at 60 mph? 
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otter
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Re: Racetrack Hint and Answer
« Reply #2 on: Aug 20th, 2002, 12:46pm » |
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on Aug 15th, 2002, 6:41am, Geremy wrote:| Doesn't the Person have to travel Infinitely fast on the second lab to keep his average at 60 mph? |
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Perhaps from a purely mathematical point of view. However, since infinite speed is not realistically possible, and keeping within the bounds of the original question (it does say you are driving your new sportscar), I think my answer still stands.
otter 
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We shall not cease from exploration. And the end of all our exploring will be to arrive where we started
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Jeremy
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Re: Racetrack Hint and Answer
« Reply #3 on: Aug 30th, 2002, 4:03pm » |
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ok... so i'm having trouble understanding this riddle. maybe someone can help me expalin it. i though the first 2 posters were idiots because i though, "hell, go 90 and 90+30/2=60!" ok yeah but then i thought about it. i toyed with making the race track 90 miles long, and bla bla bla... ok so to make a long story short, the equation for the speed he need to do on his second lap is this : let c = the track length.
(2 laps) 2c/(c/30+c/x)
so distance divided by time, 2 lengths of the track divided by the time it took him, track length divided by 30, plus track length divided by some speed).
now i started off with a nice round number, and stuck 90 in for his second speed. 45. ok, then 150 : 50... and then 9,999 (avg speed 59.82) so yeah, there's a limit at 60 mph... but yeesh, why? crackers.
i can see the similarity between this equation and 1/x, but ... ok one sec (i'm literally doing work as i write this). ok, so i simplified my orignal equation to 60x/(x+30) the c's ended up canceling each other out in the end. ok... so now it's a littlbe more obvious, the limit. x can't equal -30 because that would put a 0 in the denominator... and right... so how do i figure out where the asymtope is on the y axis? umm... oh, do you switch x and y? lets see, no that's the inverse equation... crap
AHHHHHHHH ok ok i got it.... so you got the equation
60x/(30+x)... so the way you would get an average of 60 mph is if the top number is EXACTLY 60 times greater than the bottom number. but that 30 throws you off... so even if you have an insanley large number, the 30 is going to offset the bottom number enough so that the numerator can never be EXACTLY 60 times more.... right
so thanks for bearing with me. i guess the trick is you can't double your average speed if you stay on the same race track. x/the time it took you to do one lap is 30mph... and if you double x, the only way to double your speed would be to plug in the exact same number as you did for a single lap... so the time to finish the second lap would have to be 0... and no matter how fast you go you'll never finish it in 0:00:00.... ok LKSAJFLKF
GREAT thanks for letting me struggle with this, i can sleep now tonight
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rmsgrey
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Re: Racetrack Hint and Answer
« Reply #4 on: Apr 15th, 2003, 8:58am » |
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On the plus side, if you did manage to average 60mph over the two laps, you'd probably get in a few more laps before anyone noticed!
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aero_guy
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Re: Racetrack Hint and Answer
« Reply #5 on: Apr 15th, 2003, 3:33pm » |
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If you include relativity, then you only need to go c.
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towr
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Re: Racetrack Hint and Answer
« Reply #6 on: Apr 15th, 2003, 11:12pm » |
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That depends on what reference frame your timer is in..
I don't think racers can officially time themselves..
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aero_guy
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Re: Racetrack Hint and Answer
« Reply #7 on: Apr 15th, 2003, 11:16pm » |
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Oh, well, then take all the fun out of it. Heck if you can time yourself and you believe in that whole time going backwards faster than the speed of light you can get any final answer you want.
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Boody
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Re: Racetrack Hint and Answer
« Reply #8 on: Apr 16th, 2003, 4:36am » |
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on Apr 15th, 2003, 3:33pm, aero_guy wrote:| If you include relativity, then you only need to go c. |
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If you include Quantum Mechanics you can take the tunnel, it's fast, and that will make some effect. 
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Icarus
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Re: Racetrack Hint and Answer
« Reply #9 on: Apr 16th, 2003, 8:21pm » |
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Actually, no. Tunnelling cannot exceed the speed of light. (Some probability waves do, but it can be shown that neither matter or information can be sent faster than light this way.)
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towr
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Re: Racetrack Hint and Answer
« Reply #10 on: Apr 16th, 2003, 11:23pm » |
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Tunneling takes a shortcut.. While not strickly going faster than light, I do think it can help you arrive at your destination faster than when you would travel via the normal route with the speed of light..
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Icarus
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Re: Racetrack Hint and Answer
« Reply #11 on: Apr 17th, 2003, 6:18pm » |
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As I just said: NO - it does not. The average speed at which something travels is the distance traveled (in normal space - which tunnelling does not leave, despite its name) divided by the time it takes to get there. The speed of light is not violated by tunnelling for either information or actual matter. It is violated by some of the probability wave, but this has been demonstrated not to provide a way for even information to violate the speed of light.
So, barring some as-yet unknown physics, the fastest way to get anywhere is at light speed. There are no exceptions.
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I wonder: Which is larger
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LZJ
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Re: Racetrack Hint and Answer
« Reply #12 on: Apr 17th, 2003, 6:30pm » |
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Something trivial: light speed in a vacuum, not light speed 
For example, Cerenkov radiation...
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Boody
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Re: Racetrack Hint and Answer
« Reply #13 on: Apr 18th, 2003, 8:14am » |
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on Apr 16th, 2003, 8:21pm, Icarus wrote:| Actually, no. Tunnelling cannot exceed the speed of light. (Some probability waves do, but it can be shown that neither matter or information can be sent faster than light this way.) |
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Yes, I know that Icarus.
No information can exceed ligth speed.
(in my memory : Maxwell Equations -> Lorentz transformation equations -> 'c' is speed limit)
(Phase velocity could be greater than 'c' but there is no information in it,
and in EPR paradox there's no information but correlation).
I just wanted to make a play on words with 'tunnel' an 'effect'.
But tell me, in your opinion, if you're travelling at the speed of the light, with your new Porsche, are your car-lights still enlightening ? 
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| « Last Edit: Apr 18th, 2003, 8:26am by Boody » |
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