Hm. I've thought of something that makes your answer correct, but don't yet have a way of expressing it...I still stand by my answer
Simple Puzzle
- Thread starter Trazor
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That's so not you Softus.
Er, I have a cold. And a bad back. And there's been a flood, a power cut, and a plague of locusts.
Luxury!
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Don't you start.Was there a conveyor on the mountain path?
I disagree with your disagreement.
Try imagining then, that someone replicates Bob's Day 1 journey exactly on Day 2. He will pass Bob at some point, thus proving that he was in the same point at the same time once.
Upon reflection, so do I.
I'm trying to do that, and I'll let you know how I get on.
The answer is that it is a 100% certainty if the route up is the same as the route down and within the same time scale; ie 6 hrs. The question does not require a specified time or place in the answer.
As described previously, the best way to prove it is to treat the 2 journeys as though they happened concurrently: 0600 hrs, start at the the bottom and go up and simultaneously start at the top and go down. Whatever the speeds used, the 2 journeys will pass each other, somewhere, at a random moment, once. This must happen because both journeys last exactly 6 hrs. That place and time will be the only common place and time in both journeys.
As described previously, the best way to prove it is to treat the 2 journeys as though they happened concurrently: 0600 hrs, start at the the bottom and go up and simultaneously start at the top and go down. Whatever the speeds used, the 2 journeys will pass each other, somewhere, at a random moment, once. This must happen because both journeys last exactly 6 hrs. That place and time will be the only common place and time in both journeys.
Yes, the answer is, its a certainty..
Provided start and end times are the same, and EXACTLY the same route is taken. then they must meet, thus same point/same time of day.
The 2 journeys could be years apart, but still the same result.
The easiest way to see it, is to give Bob a twin, and do both journeys on the same day.
An E-beer to all who got it right.
Provided start and end times are the same, and EXACTLY the same route is taken. then they must meet, thus same point/same time of day.
The 2 journeys could be years apart, but still the same result.
The easiest way to see it, is to give Bob a twin, and do both journeys on the same day.
An E-beer to all who got it right.
I would like to challenge your answer.
Same journey, same route, random speeds, ok?
Lets say the mountain is 600 metres high.
Day 1, he takes
2 hours to reach 100 metres-time =08.00
1/2 hour to reach 200metres-time =08.30
1 hour to reach300 metres-time=09.30
1/2 hour to reach 400 metres-time=10.00
1 hour to reach 500 metres-time=11.00
1 hour to reach 600 metres-time=12.00
Total time taken = 6 hours.
Day 2 he takes,
2 hours to reach 500 metre mark-time=08.00
1 hour to reach 400 metre mark-time=09.00
1 hour to reach 300 metre mark-time=10.00
1/2 hour to reach 200 metre mark-time=10.30
1 hour to reach 100 metre mark-time=11.30
1/2 hour to reach base level-time = 12.00
At no time does he pass the same spot at the same time therefore there is no certainty that he will which means the odds are 50/50.
Same journey, same route, random speeds, ok?
Lets say the mountain is 600 metres high.
Day 1, he takes
2 hours to reach 100 metres-time =08.00
1/2 hour to reach 200metres-time =08.30
1 hour to reach300 metres-time=09.30
1/2 hour to reach 400 metres-time=10.00
1 hour to reach 500 metres-time=11.00
1 hour to reach 600 metres-time=12.00
Total time taken = 6 hours.
Day 2 he takes,
2 hours to reach 500 metre mark-time=08.00
1 hour to reach 400 metre mark-time=09.00
1 hour to reach 300 metre mark-time=10.00
1/2 hour to reach 200 metre mark-time=10.30
1 hour to reach 100 metre mark-time=11.30
1/2 hour to reach base level-time = 12.00
At no time does he pass the same spot at the same time therefore there is no certainty that he will which means the odds are 50/50.
Ah yes - I've seen the light.
What you mistakenly wrote was this:
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.
Whereas, apparently, what you meant to write was this:
Bob climbs a mountain. Meanwhile, Bob's twin brother descends the same mountain. Both start at 06.00 hrs, on the same day, and reach their destinations by noon-12.00hrs. The paths they take are identical, except in opposite directions.
What are the chances that Bob and his twin meet, and that there is no rip in the spacetime continuum at the moment they meet?
Answer: 100%.
Draw a graph.
Height on the vertical axis, 0 - 500m.
Time on the horizontal axis, 0 - 6 hours, or 06:00 to 12:00 hours.
Plot a wibbly wobbly line for the ascent from bottom left of graph to top right.
Plot another wibbly wobbly line for the descent from top left of graph to bottom right.
The lines must cross. The point where they cross is at equal height and equal time...
edit! vertival removed , vertical inserterated.
Height on the vertical axis, 0 - 500m.
Time on the horizontal axis, 0 - 6 hours, or 06:00 to 12:00 hours.
Plot a wibbly wobbly line for the ascent from bottom left of graph to top right.
Plot another wibbly wobbly line for the descent from top left of graph to bottom right.
The lines must cross. The point where they cross is at equal height and equal time...
edit! vertival removed
, vertical inserterated.
Using your figures, consider the following...
If on the climb he takes 15 minutes to reach the first 50 metres.
Then on the descent he reaches 100 metres form the bottom after 5 1/2 hours, then their is a 15 minute period during which they will cross.
blondini has it right, but here is an even simpler way to look at the solution....
Draw 2 identical pyramids, and draw a straight line down from the top point, on each picture.
As the route is EXACTLY the same we can use a straight line.
Mark one picture feb 1st, mark one picture feb 2nd.
Put them side by side.
Put a pencil at the top of one mountain, and a pencil at the bottom of the other mountain.
Start your journey at the same time of day, you will find it impossible not to pass each other at the same time of day, albeit on the separate pictures.
Ah yes - I've seen the light.
But what you meant to write was...
As I dont't understand the solution (even though I'm sure it is correct)
I will conjure up my own question, and answer it correctly, thus proving that I do know that 2+2 =4.
But what you meant to write was...
As I dont't understand the solution (even though I'm sure it is correct)
I will conjure up my own question, and answer it correctly, thus proving that I do know that 2+2 =4.
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