Simple Puzzle

[Trazor]

Bob climbs a mountain, He starts at 06.00 hrs at the bottom of the mountain.
He climbs with varying speeds and reaches the top of the mountain by noon-12.00hrs.

Having done enough mountaineering for a day, he decides to enjoy the scenery and take the remaining day off on the peak.

The next day, exactly at 06.00hrs sharp, he starts to climb down again using exactly the same path, which he had taken the previous day.
Again the speed of descent is totally random.
He manages to reach the bottom from where he started a day earlier exactly at 12.00 hrs noon.

Given the above, what are the chances of Bob being on the same point of the mountain at exactly the same time of day, on both days.

 

[imamartian]

random speeds?....... then it's 50/50 isn't it?

 

[nrgserv]

50:50

 

[regsmyth]

Oh come on, the actual chances of being at the same spot on the mountain, at the same time, as on the previous day - just about nil.

 

[Spark123]

I'll go with just about nil also, the only point which it can happen for is once when he passes around the half way point. Taking into account the varying speeds reduces the probability of this happening 24hrs apart to about nil.

 

[Softus]

what are the chances of Bob being on the same point of the mountain at exactly the same time of day, on both days.

It depends on your definition of the word "point".

 

[blondini]

... what are the chances of Bob being on the same point of the mountain at exactly the same time of day, on both days.

100% absolute certainty.

 

[tim west]

Given the above, what are the chances of Bob being on the same point of the mountain at exactly the same time of day, on both days.

Depends on whether the ferry turns up on time or not, is this a homework problem?

 

[johnny_t]

Bob climbs a mountain, He starts at 06.00 hrs at the bottom of the mountain.
He climbs with varying speeds and reaches the top of the mountain by noon-12.00hrs.

Having done enough mountaineering for a day, he decides to enjoy the scenery and take the remaining day off on the peak.

The next day, exactly at 06.00hrs sharp, he starts to climb down again using exactly the same path, which he had taken the previous day.
Again the speed of descent is totally random.
He manages to reach the bottom from where he started a day earlier exactly at 12.00 hrs noon.

Given the above, what are the chances of Bob being on the same point of the mountain at exactly the same time of day, on both days.

100% Certainty of it happening once.

Imagine that instead of it being Bob going up one day, and Bob coming down the next, it is two different people doing the two journeys on the same day.

They must pass somewhere....

 

[Softus]

100% Certainty of it happening once.

I disagree.

Imagine that instead of it being Bob going up one day, and Bob coming down the next, it is two different people doing the two journeys on the same day.

That's a different scenario.

Why do people introduce alternative scenarios in an attempt to prove invalid reasoning?

They must pass somewhere....

Yes, but now "imagine" your scenario being run on two different days, with the random speed factor - will your two people pass on the second day at the same place that they did on the first?

 

[AndrewSchofield]

They must pass somewhere....

True... but he's doing the two journeys on two seperate days and there's no certainty thay he'll reach the same point AT THE SAME TIME OF DAY.

 

[blondini]

Let's not make a mountain out of a, er, um, er...

Cough! I stand by my answer.

 

[Softus]

I stand by my answer.

Hm. At what time would that be, and/or where would that point (sic.) be?

 

[nrgserv]

Cough! I stand by my answer.

me too.
he either will be at the same spot sometime on the hill, or he wont.
2 chances.
50:50

 

[blondini]

I stand by my answer.

Hm. At what time would that be, and/or where would that point (sic.) be?

Those questions can't be answered from the data given.

I still stand by my answer