One for you to ponder over the festive season.
Exactly 100 miles due south of Town A lies Town B. Being in the USA it is connected by a straight, undulating highway.
Exactly 50 miles due east of Town C lies Town D. The towns are connected by a straight railway.
Where the road intersects the railway line is a manned level crossing.
Jones, a resident of Town A sets out one day in his standard automobile, to drive to Town B.
At the same time, a train and carriages leave Town D to travel to Town C.
Three quarters of the way into their journey when both transports are an equidistance from the level crossing, Jones can see the train coming from his left across the plain.
Likewise the train driver sees Jones's car to his right.
Both decide at the same time to increase speed to their maximum of 74.34 mph and this is the speed they reach and maintain when both are an equal distance of 1 mile from the level crossing.
The Crossing Keeper is fast asleep in his Signal Box and remained so throughout leaving the barriers up..
Both Jones and the Train Driver believe they can reach the Level Crossing before the other. They race forward at their maximum speeds which they maintain believing they would reach the Level Crossing before the other.
The final mile and a half to the crossing is absolutely level There was no wind. It was calm.
Jones got across.
The question for you mathematicians is, how did Jones manage this. A reminder that speed equals distance over time.
dvd
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DVD - I am old enough not to mind being called dim, or worse! We know the relationship, in distance and direction between A and B, and between C and D. Where are C and D relative to A and B? At the moment we don't have information to tell us that the road and the railway even cross each other - or do we?
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While you're all thinking about DVD's conundrum, try this one as well, all the way from the USA where I am currently basking in warm afternoon sunshine with clear blue skies - and that's just in NY State :
You are driving in a car at a constant speed. On your right is a sheer drop with no barrier, and on your left is a fire engine travelling at almost exactly the same speed as you. In front of you is a galloping horse which is the same size as your car and you cannot overtake it. Behind you is another galloping horse. Both horses are also travelling at the same speed as you .
What must you do to get safely out of this highly dangerous situation?
With best wishes to HJ and all the regular Back Roomers for Christmas and the New Year - I still can't bring myself to say"Happy Holidays" - and thank you for keeping me so well in the picture on the UK motoring front.
Jack
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Jack
Wait until the attendant switches the roundabout off....?
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What must you do to get safely out of this highly dangerous situation?
Blow your horn and hope the horse veers either into the fire engine or over the ravine taking its pesky genes with it.
Horses; better on the dinner plate than in the road ...
Hawkeye
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Stranger in a strange land
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Because, being America, Jones is driving in the right-hand lane, the train is coming from his left and the rear of his car would thus have cleared the potential impact zone before the front of the train entered it.
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Whilst the reason is obvious, I will have to sit down to do the arithmetic to prove to the doubters why!
The answer is that the time at which they are both an equal difference from the crossing (1 mile) and travelling at the same speed is not the actual same time!
20 secs.
Happy Xmas
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pmh (was peter)
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Sorry distance NOT difference.......
Too much French red at lunchtime (or do I need to to top it up!)
--
pmh (was peter)
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Jones got across.
Across on hisgrave?
Hawkeye
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Stranger in a strange land
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The train driver is a member of the NUR. Bob Crowe called him out on strike and he never made the crossing.
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TourVanMan TM < Ex RF >
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I think Hawkeye got it. In the churchyard.
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I know Screwloose got it - Well done - the answer is indeed to wait until the roundabout stops!
Jack
PS Did he know, or did he work it out .....!?
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Jack
It's the two horses that gave it away; too surreal. Makes you think gallopers/roundabout etc..... [Well me; anyway...]
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As this is utterly non motoring-related, I'll understand if it's deleted. However, it's my favourite brainteaser (amongst the thousands clogging up my brain) and I'd like you to have a go.
Two tennis professionals, A and B, are playing in a lawn tennis tournament.
Player A has just served six aces in a row. Player B has not hit the ball at all in all that time. No returns, no serves. However, player B is still winning the match. What are the odds that her parents are divorced?
V
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Time to put you all out of your misery:
Using S= T over D then:
D(Sa,Sc)<= D(Sa,Sb)+ D(Sb,Sc) and
D(Sa,Sb)=D(Sb,Sa) with
D(Sa,Sa)=0 (arrival at level X)
The answer is:
roll of drums and trumpet fanfare..........
HIS WIDOW BOUGHT HIM ONE
Well done Hawkeye - must be the Hunton air?
dvd
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There are several inconsistencies and ambiguities in this story:
1) "Where the road intersects the railway line is a manned level crossing" has to be presumed to mean the road A-B and the railway C-D. The OP does not actually say that. All we are told is that both are somewhere in America, although in sight of each other at some point.
2) The road is stated to be undulating. That is not consistent with the statement that the final mile and a half to the crossing is dead flat.
3) If the road really is undulating, a measured horizontal mile along the road would take longer than the same horizontal distance along the railway even if they were both travelling at the same (wheel) speed.
4) It implies, but does not state, that the moment when they both decided to increase speed was after the point when they were 3/4 through their journeys. It could have been beforehand.
5) Does 3/4 of the way into their journey (sic - why singular ?) mean by time or distance? And if time, does it mean time at their original speeds, or time allowing for their increased speeds?
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DVD
Er; where does it say that Jones was married?
Your calculations may prove that, accepting the given "equal speed and distance from the level crossing" fact, the two protagonists do indeed reach the CROSSING at the same time. But that's not the "crossover point."
How wide is an American "two-lane blacktop" railway crossing: 30 feet? If Jones is, understandably, crossing at the extreme far side from the train's entrance: [much is made of the "looking left - looking right" etc.] then the front of the train has an extra 23[?] feet to travel to reach the intersection zone - which the front of Jones car is already entering.
Both are travelling at the same 109ft.sec; meaning that if Jones 14 ft[?] car can clear the intersection zone [front to rear bumper, plus the width of the train's bogie - 7 ft?] then he makes it - free and clear - and that's using the exact given facts....
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Ok nice one!
However Cliff is correct in his assertions, but 3/4 of the 'way' MUST mean distance.
The rates of acceleration from this point to max speed are extremely unlikely to be the same, hence my answer stands in principle. In detail I believe there are an infinite number of possible solutions. One subset of which will produce the opportunity for the wife to buy the cross!
Unlike DVD to produce something with inconsistencies and ambiguities!
Happy Xmas.
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pmh (was peter)
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Well done Hawkeye - must be the Hunton air? dvd
Catterick Village air.
I claim my prize of a pootle up to Hawes on the V-Strom once all the Christmas hangers-on have vanished :-)
Hawkeye
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Stranger in a strange land
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