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dpellerin

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Reply with quote  #1 
PART C: Travel *and* Math

A train leaves Penzance, a beautifull town near the tip of the Cornish peninsula, en route to Camborne, at 5:00 PM Greenwich Mean Time. Denzil Trevithick may or may not be on this train. The diesel motor on this train has a peculiar ability allowing the train to go from 0 to 40 miles per hour in 0.0 seconds. In then chugs along the tracks at a steady 40 miles per hour neither slowing down at level crossways for the red light nor speeding up at crossways to make the yellow light safely like many motorists tend to do.

Another train leaves Camborne en route to Penzance at 5:00pm Greenwich mean time (i.e. at the precisely the same time as the Penzance-Camborne train departure).  Note that there are more than 400 reasons to visit Penzance for shopping and they are all located and listed in the Shopping Guide while hundreds of gastronomic choices await the passengers on the Camborne-Penzance train at Penzance's many RestaurantsIts mean speed, minimum speed and maximum speed along the Camborne-Penzance route is a steady 30 miles per hour as it is also equiped with that same peculiar diesel engine as the Penzance-Camborne train.

As soon as the train leaves Penzance, Julian Tredinnick (aka Jubags69) starting at the front of the locomotive takes flight on his skateboard and travels at 60 miles per hour along the track towards Camborne neither slowing down to admire the beautiful view of St. Michaels Mount nor speeding up when going downhill (somehow the law of gravity does not apply here). He is so nimble that he goes from 0 to 60 in 0.0 seconds. Given the high speed, we can safely assume that he is wearing his ear muffs and/or earplugs as well as a heavy duty helmet. He barely glances at the gaping holes of the abandonned tin mines along the route, those same mines for which the Greek Pytheas undertook a perilous journey in 330 BC from the Mediterannean Sea having to cross a blockade set by the Carthaginians at the Strait of Gibraltar.

In the mean time, the Camborne-Penzance train is approaching Julian at the relative speed of 90 miles an hours which is the train's speed (30) + Julian's speed (60). Now when Julian reaches the Camborne-Penzance train, he does an abrupt about- face and travels in the opposite directions from whence he came without ever slowing down. He skates at a steady 60mph speed, aproaching the Penzance-Camborne train at the relative speed of 100mph (40+60) until he reaches the Penzance-Camborne train and again does another about face.

This extremely skilled skateboarder does the back-and-forth each time he meets the oncoming train up until the two trains meet at which point Julian nimbly picks up his board and jumps off the track out of the way of both trains. Lest someone makes the wrong assumption here, allow me to point out that there was no train crash as the British National Railway System is quite safe and had the two trains running on separate tracks.

i) Assuming a 13 mile distance between Penzance and Camborne, what is the total distance that Jubags69 traveled on his skateboard during his back and forth ralies between the trains from departure until the two trains meet?

10 points have already been awarded to Jubags69 in deference to his daring feat of daredevils and skills.

ii) Assuming that at each turnabout, Jugabs69 is able to *grab* a passenger hanging from the locomotive door or window (as Denzil Trevithick was in Jugabs69's solution to SAT 5A and 5B) and transport the passenger towards the opposite train and transfer him/her onto the train at the next turnabout point, how many passengers would have to be in each train at departure and how many passengers would Jugabs69  need to transfer from one train to the other and/or from each train to an abandonned platform between the trains in order to provide a NEW solution to SAT question 5A and 5B all the while keeping his speed at a steady 60 mph?

dp
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jubags69

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Reply with quote  #2 
If the rain storm that hit this morning as I was on my motorbike on the way to work had not soaked through my leather trousers so badly I may be able to detect if I did actually wet myself or not.

Class.

I will re-read this at length later but at the moment I am assuming everything will be rlative to the number of isotonic jelly beans consumed on each leg (only orange and lemon flavor available in the UK I think the US has a better range)... I will have to test and get back to you...



Ju

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LynnMcLaren

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Reply with quote  #3 

Hi Dp, ((( Smiles )))

 

I'd say so..

 

Quote:
10 points have already been awarded to Jubags69 in deference to his daring feat of daredevils and skills.

 

What a brave guy indeed.. Motorbike HUH ? In the rain no less.. Oh scarry..

I'm totally intrigued...

 

I'm not good at theses intricate skill quizing thought provoking contests... 

 

But I just had to take a peek and I do agree.. It does take skill. I went to a fair that had a skate park.. All cement.... Helments but no knee pads..

 

Did thoses guys go.. And did anybody fall... Yes... Is falling on cement fun.. NO... But it was interesting neverless to watch them go... With two feet firmly on the ground.. But boy.. Was that music they skated too... Loud...

 

And thoses speakers were real big.......

 

I wonder how many of them will develope tinnitus or hyperacusis when they grow up... Thought provoking indeed... What the future may hold for them...

Who will mentor to the very young... Will the hyperacusis board still be here.. Will they find the cure or develope bionic ears and efferent nerves and super sonic brains to replace it all by then.....

 

Only time will tell.....  

 

Untill then... Ju rules the day....... Hyperacustic on wheels.. And getting better everyday...

 

Great story Dp.... (((( Smiles )))) 

   


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Lynn
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Reply with quote  #4 

Cute.

 

Lots of distractors!

 

OK.  First consider the speed of the trains.

 

Train A travels at 40 miles per hour.

Train B travels at 30 miles per hour.

 

Next consider the time that it takes for the two trains to (almost) collide.  That time will be the same for both trains - call it "t."

 

How far will train A travel in "t" hours?  Train A will travel 40t miles.

How far will train B travel in "t" hours?  Train B will teavel 30t miles.

 

Finally consider the distance.  We know that the distance that Train A travels plus the distance that Train B travels before the two trains (almost) collide is 13 miles.

 

Thus, 40t+30t=13

So, 70t=13

And therefore, t=13/70 hours (or 0.1857 hours)

 

Well, if ol' Julian is skateboading along at 60 miles per hour (back and forth between to the locomotives), how far does he skateboard during the 0.1857 hours it takes before both trains (almost) collide?  That would be 60x0.1857 miles - or 11.14 miles.

 

How'd I do so far?

 

sp

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dpellerin

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Reply with quote  #5 
SP,

You did very well and eliminated the unnessary information (almost). Your answer is correct. 10 points for the answer.

However, you did one extra step that was not required.

Since Julian and the trains travel for the same amount of time and at constant speed, t need not be calculated.

t=distance/speed

t=distance(ju)/60=distance(trains)/(30+40)

hence distance(ju)=distance(trains)*60/(30+40)

i.e. 60/(30+40)*13 miles =11.14 miles

Since the point of this exercise is to arrive at the answer with the least amount of work, 3 points subtracted for the unnecesary step!

dp

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Reply with quote  #6 

Most folks would have trouble following your logic, sound as it might be.  I explained it step by step for THEM, not for YOU.  (Othrewise, why not do it in your head and just post the answer??!!)  So I'll take my three points back and depend on your integrity to subtract them from any future score that you might amass. 

 

sp

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dpellerin

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Reply with quote  #7 
Sp

Seems we cross posted as I added three lines in my post.

What part of the logic would you say is beyond the scope of the regular person?

dp

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Reply with quote  #8 

This sentence, dp:

 

"Ju's distance can be calculated simply by using the ratio of his speed to the trains' relative speed multplied by the total distance covered by the trains."  There's nothing "simply" about that sentence for the average guy or gal.

 

Most everybody learned about ratios in grade school - but I daresay most have not used the concept as you have in years.

 

Never mind - keep the three points.  Gives you a feeling of power? 

 

sp

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dpellerin

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Reply with quote  #9 
OK your point taken (no pun intended here) . Then I've removed that sentence from my post.

Just follow the rest.

I have just deducted 3 points from my already negative balance!

dp


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