ekt_bear:

OK. So what if:
a) His speed is not constant. Say he is accelerating at 1 meter/second^2 or something.
b) he doesn't walk at the same speed going up the hill as down the hill. So pretend he goes up the hill with velocity 1 m/s, but down the hill with velocity 2 m/s.

What then? Is it still true that there is some time at which he is at the same spot on both days?

You are on the right track though...push it further and see if you can generalize.


When I solved the problem, I did so using math. But you can actually solve it using elementary reasoning too.

without knowing his speed, it's impossible to give a definite answer.
Assuming the same speed on both days, yes.
If he descends the hill at twice his ascension speed, possibly, depending on the distance from his home to the top of the hill.

Stpirate: Make I See Who Sabi Solve Maths here
10 + 0 * 10 + (10 * 0 + 10) - 5=
Mathematicians Do Your Thing Lol.

Someone answered

Ans = 5

sauer: Question:
The marvel hero, Flash is to run against a tortoise. He gives the tortise a head start. So after tortoise gets to point A, Flash starts to run to catch up with the tortoise. But the claim is that Flash will never catch up with Mr. Tortoise. How then? Flash has to get to point A before we can say he's caught up with tortoise. But by then, Mr. Tortoise is in point B, i.e. point B - A ahead. Flash has to run that distance. When Flash gets to point B, Mr. Tortoise is now in point C. So, it goes and Flash never catches tortoise. Can someone logically explain whatz happening?

The tortoise doesn't exist.

sauer: Question:
The marvel hero, Flash is to run against a tortoise. He gives the tortise a head start. So after tortoise gets to point A, Flash starts to run to catch up with the tortoise. But the claim is that Flash will never catch up with Mr. Tortoise. How then? Flash has to get to point A before we can say he's caught up with tortoise. But by then, Mr. Tortoise is in point B, i.e. point B - A ahead. Flash has to run that distance. When Flash gets to point B, Mr. Tortoise is now in point C. So, it goes and Flash never catches tortoise. Can someone logically explain whatz happening?

There's more than one tortoise or the distance between point 0 and point A is much greater than the distance between points A-B, B-C ...............

ekt_bear: Q:
There was an Ijebu man who lived near a hill.

Every Monday morning @ 9am, he would walk a path from his home to the top of this hill, meditate and pray.

Then Tuesday morning @ 9am, he would walk the same path from the top of the hill back to his home.

Is there any time at which he crossed the same spot on both Monday and Tuesday?

The time definitely has to be 9am since there are no other variables involved...

Since you didn't tell us the actual time he gets home on Monday, however, you told us the time he leaves the hill on Tuesday...

And the constant is 9am...

9am -

sauer: Question:
The marvel hero, Flash is to run against a tortoise. He gives the tortise a head start. So after tortoise gets to point A, Flash starts to run to catch up with the tortoise. But the claim is that Flash will never catch up with Mr. Tortoise. How then? Flash has to get to point A before we can say he's caught up with tortoise. But by then, Mr. Tortoise is in point B, i.e. point B - A ahead. Flash has to run that distance. When Flash gets to point B, Mr. Tortoise is now in point C. So, it goes and Flash never catches tortoise. Can someone logically explain whatz happening?

Point A is the finish line - the others don't exist....

some-girl:


without knowing his speed, it's impossible to give a definite answer.

Not true. Read the post I made earlier where I gave away the answer.

shymexx:

The time definitely has to be 9am since there are no other variables involved...

Since you didn't tell us the actual time he gets home on Monday, however, you told us the time he leaves the hill on Tuesday...

And the constant variable is 9am...

9am -

Nope. The point of the problem is not to say, "the time is X"...the value of X will change depending on what the velocities are.

The problem is about arguing about why a time must exist, not saying what it is.

ekt_bear:
Nope. The point of the problem is not to say, "the time is X"...the value of X will change depending on what the velocities are.

The problem is about arguing about why a time must exist, not saying what it is.

Let's say he starts to meditate and pray on Monday @9am, he ends the same session at 9am on Tuesday..

Hmmm... It should be the time he's walking-down/gets-to-the-top the hill...

Since you didn't provide the time he either leaves the hill on Monday, or gets there on Tuesday... I guess he meditates and prays from the time he gets to the top of the hill on Monday till he leaves the same spot on Tuesday... So, 9am is the fixed constant - and he uses the point-of-entry and point-of-exit at the same time, isn't it?

nah. read the explanation i gave earlier in this thread.

Essentially you can transform the problem into one where there is a second Ijebu man who walks down the hill on Monday @ 9am, just as our original guy walks up the hill at 9am.

No matter the speed/velocity of the 2nd Ijebu guy, they will eventually cross paths at some time.

ekt_bear: nah. read the explanation i gave earlier in this thread.

Essentially you can transform the problem into one where there is a second Ijebu man who walks down the hill on Monday @ 9am, just as our original guy walks up the hill at 9am.

No matter the speed/velocity of the 2nd Ijebu guy, they will eventually cross paths at some time.

Let's say there's one path to climb and walk down the hill... So, they'll meet at the point where they'll either climb, or walk-down the hill - that's the point of intersection...

ekt_bear: nah. read the explanation i gave earlier in this thread.

Essentially you can transform the problem into one where there is a second Ijebu man who walks down the hill on Monday @ 9am, just as our original guy walks up the hill at 9am.

No matter the speed/velocity of the 2nd Ijebu guy, they will eventually cross paths at some time.

Of course they WOULD definitely cross paths at some point. However, that wasn't your question, your question was "Is there any time at which he crossed the same spot on both Monday and Tuesday?"

Without knowing his speed in either direction, it is not possible to tell if there is such a time.

some-girl:


Of course they WOULD definitely cross paths at some point. However, that wasn't your question, your question was "Is there any time at which he crossed the same spot on both Monday and Tuesday?"

Without knowing his speed in either direction, it is not possible to tell if there is such a time.

My dear, if there exists a SPOT where they cross paths, then necessarily there exists a TIME, right?

So how can you say it is impossible to tell if there is such a time?

Like I keep saying, the speed he goes in either direction is irrelevant to the existence of a time.

ekt_bear:

My dear, if there exists a SPOT where they cross paths, then necessarily there exists a TIME, right?

So how can you say it is impossible to tell if there is such a time?

Like I keep saying, the speed he goes in either direction is irrelevant to the existence of a time.

Your question was interpreted to have asked if there was a particular time when the man or both men were at the same spot.

e.g 20m from his home at 11am on both Monday and Tuesday.

Hence my very first response:

Let's say the journey to the hill top takes a total of 2 hrs
Assuming he walks at the same speed all the way to and fro.

At 10am on Monday and Tuesday, he'd be halfway between the his home and the hill top.

What you now seem to be asking is whether they would have crossed paths at any time which is a different question.

some-girl:


Your question was interpreted to have asked if there was a particular time when the man or both men were at the same spot.

e.g 20m from his home at 11am on both Monday and Tuesday.

Yes.

What you now seem to be asking is whether they would have crossed paths at any time which is a different question.

They are secretly the same question.

Or more precisely, my question "is there a time?" can be answered by observing that their paths must cross at some time.

Like, if you:
a) transform the problem from one Ijebu man going up the hill Monday and down Tuesday to two Ijebu men on the same hill, one walking up the hill the other walking down the hill
b) observe that in the latter situation, the paths must cross eventually at some position x on the hill
c) associate with this position x is a time T at which the guy walking up the hill hits x

then you are able to answer the original question with "Yes, of course, because of (a), (b) and (c) above."

Do you see the logical steps here, how we are able to go from asking about a time to asking about a position?

ekt_bear:
Yes.



They are secretly the same question.

Or more precisely, my question "is there a time?" can be answered by observing that their paths must cross at some time.

Like, if you:
a) transform the problem from one Ijebu man going up the hill Monday and down Tuesday to two Ijebu men on the same hill, one walking up the hill the other walking down the hill
b) observe that in the latter situation, the paths must cross eventually at some position x on the hill
c) associate with this position x is a time T at which the guy walking up the hill hits x

then you are able to answer the original question with "Yes, of course, because of (a), (b) and (c) above."

Do you see the logical steps here, how we are able to go from asking about a time to asking about a position?

That answers a different question i.e at what time/ point will they cross paths.

What your first question asked is if there was a particular time when a man would be at the same spot he was on the previous day. e.g at 11am on Tuesday, he is at the same spot he was at 11am on Monday.

More information would be required to answer the above correctly.

Your question is not far from being ambiguous.

Sigh.

The answer to, "is there a particular time when a man would be at the same spot he was on the previous day" is yes.

Why? Because of reasons (a), (b) and (c) above.

Like I feel that you aren't reading or thinking about my explanations at all. Think about each of steps (a) (b) and (c) carefully, so that it makes sense to you why we can say "Yes" ot the question in red text.

There is nothing ambiguous here...either the answer is "yes", "no", or "it depends."

And because of (a), (b) and (c), the answer is "yes."

the answer to your previous question is perhaps.
the answer to your recent question is yes.

Ekt_bear, this is mathematics - and there's no guess work...

And since 9am is the constant, then obviously the time would be 9am at the point of climbing and leaving the hill...

Anything aside that is utter tosh!

X goes to a place @9am

X leaves the same place @9am

9am is the fixed constant!

some-girl:
the answer to your previous question is perhaps.
the answer to your recent question is yes.

Lord Jesus.

1. Suppose that there ISN'T a time when he reaches the same spot.

2. Then there ISN'T a time for which the two-Ijebu man scenario reaches the same spot (if there was a time T in the two Ijebu man scenario, use that time T for the original problem!)

3. If there isn't a time for the two Ijebu man scenario, then this means that somehow the first guy walks up the hill and the second guy walks down the hill, and they NEVER bump each into each other, despite walking on the SAME path.

4. But (3) is impossible, there is no way for me to walk from point A to point B on a path and you to walk from point B to point A without us eventually meeting.


Does this make it crystal clear to you why the answer to both question is 'yes' ?

You cannot say "Yes" to one, and "it depends" or "maybe" to the other.

They are the same exact question in disguise..

ekt_bear:

Lord Jesus.

1. Suppose that there ISN'T a time when he reaches the same spot.

2. Then there ISN'T a time for which the two-Ijebu man scenario reaches the same spot (if there was a time T in the two Ijebu man scenario, use that time T for the original problem!)

3. If there isn't a time for the two Ijebu man scenario, then this means that somehow the first guy walks up the hill and the second guy walks down the hill, and they NEVER bump each into each other, despite walking on the SAME path.

4. But (3) is impossible, there is no way for me to walk from point A to point B on a path and you to walk from point B to point A without us eventually meeting.


Does this make it crystal clear to you why the answer to both question is 'yes' ?

You cannot say "Yes" to one, and "it depends" or "maybe" to the other.

They are the same exact question in disguise..

I disagree with the bolded.

No point continuing with this "debate" as I and others, I believe, can't see how two questions - "do they cross paths/ intersect at any time/ spot?"
and "Is there any time at which he crossed the same spot on both Monday and Tuesday?" are one and the same.

Do you not get that we can replace the problem I gave where there is ONE Ijbeu man who walks up the hill Monday @ 9am and then walks down it Tuesday @ 9am with another problem in which there are TWO Ijebu men, one at the bottom of the hill and one at the top, both of who start walking @ 9am?

I am just shifting the Tuesday event 24 hrs ahead to Monday in order to transform from the first problem to the second one....

ekt_bear: Do you not get that we can replace the problem I gave where there is ONE Ijbeu man who walks up the hill Monday @ 9am and then walks down it Tuesday @ 9am with another problem in which there are TWO Ijebu men, one at the bottom of the hill and one at the top, both of who start walking @ 9am?

I am just shifting the Tuesday event 24 hrs ahead to Monday in order to transform from the first problem to the second one....

All I'm saying is your initial question didn't ask for the answer you're looking for.

It wasn't clear that you were asking if they'd "jam" at some point which is inevitable if they start out at the same time and walk the same path.

ekt_bear: Q:

There was an Ijebu man who lived near a hill.

Every Monday morning @ 9am, he would walk a path from his home to the top of this hill, meditate and pray.

Then Tuesday morning @ 9am, he would walk the same path from the top of the hill back to his home.

Is there any time at which he crossed the same spot on both Monday and Tuesday?

What is unclear or ambiguous about this question?

The possible answers are:
a) YES
b) NO
c) It depends

The correct answer is (a), by the reasoning I already went through in this thread. I didn't ask if they'd jam; that is obvious, since the problem states that they use the same path.

ekt_bear: Do you not get that we can replace the problem I gave where there is ONE Ijbeu man who walks up the hill Monday @ 9am and then walks down it Tuesday @ 9am with another problem in which there are TWO Ijebu men, one at the bottom of the hill and one at the top, both of who start walking @ 9am?

I am just shifting the Tuesday event 24 hrs ahead to Monday in order to transform from the first problem to the second one....

scratchin head...

Velocity= d/t

Man1 V1=d1/t1
Man2 V2=d2/t2

when they meet t1=t2

so t1= d1/v1 and t2=d2/v2

d1/v1=d2/v2
... i am blocked

Sybellah:
scratchin head...

Velocity= d/t

Man1 V1=d1/t1
Man2 V2=d2/t2

when they meet t1=t2

so t1= d1/v1 and t2=d2/v2

d1/v1=d2/v2
... i am blocked

give the answer now, how to do it?

You're just wasting your time, love... There's no point finding the velocity since he didn't give the time the man got to the hill on Monday and the time he got back home on Tuesday... It's a simple mathematical puzzle where you've to use the mathematical constant available...

Finding the velocity will only make it more complicated and lead you to a dead end because there's none...Unless you want to do guess work...

Ekt_bear..

Give the answer!

If it isn't 9am and at the point of exit/entry - then your puzzle is the most ambiguous mathematical puzzle ever!!

Sybellah: We can try the mathematical approach, sure.

How about we call his position as a function of time on Monday x(t). So:

x(9am)=0 (bottom of hill)
x(whenever he finishes) = 1 (bottom of hill)

Let's use y(t) to denote his position as a function of time on Tuesday. So:

y(9am) = 1
y(whenever he finishes on Tuesday) = 0

So, we are looking for a time T where:

x(T) = y(T)

Or in other words, a time T such that:

x(T)-y(T)= 0

Intuitively, no matter how one reasonably chooses x(t) or y(t), there will always exist a time T for which the above equation is zero....it is impossible for x(t)-y(t) to be -1 for t=9am
and then +1 for some other value t without at some point crossing zero [size=2pt](if you want to get technical, this is something called the intermediate value theorem from calculus. But no need to bother yourself with it, we can solve this problem with just intuitive reasoning )[/size].

For example, I might choose x(t) = t^2, y(t) = 1-t. A little bit of algebra will show you that you can find a value T so that x(T)=y(T). Similarly, for any choices of x(t) and y(t) you'll be able to find a value T.

shymexx:

You're just wasting your time, love... There's no point finding the velocity since he didn't give the time the man got to the hill on Monday and the time he got back home on Tuesday... It's a simple mathematical puzzle where you've to use the mathematical constant available...

Finding the velocity will only make it more complicated and lead you to a dead end because there's none...Unless you want to do guess work...

i hear u babes

ekt_bear: Sybellah: We can try the mathematical approach, sure.

How about we call his position as a function of time on Monday x(t). So:

x(9am)=0 (bottom of hill)
x(whenever he finishes) = 1 (bottom of hill)

Let's use y(t) to denote his position as a function of time on Tuesday. So:

y(9am) = 1
y(whenever he finishes on Tuesday) = 0

So, we are looking for a time T where:

x(T) = y(T)

Or in other words, a time T such that:

x(T)-y(T)= 0

Intuitively, no matter how one reasonably chooses x(t) or y(t), there will always exist a time T for which the above equation is zero....it is impossible for x(t)-y(t) to be -1 for t=9am
and then +1 for some other value t without at some point crossing zero [size=2pt](if you want to get technical, this is something called the intermediate value theorem from calculus. But no need to bother yourself with it, we can solve this problem with just intuitive reasoning )[/size].

For example, I might choose x(t) = t^2, y(t) = 1-t. A little bit of algebra will show you that you can find a value T so that x(T)=y(T). Similarly, for any choices of x(t) and y(t) you'll be able to find a value T.

olala this is frustratin oo...let me try it again with the method u gave ...

Sometimes a picture speaks more clearly than words do:



The blue line is Monday. The green line is Tuesday.

No matter how you choose the velocities, his position is bound to intersect.

(In this plot I chose x(t) = t, so constant speed on Monday. For Tuesday, y(t) = 1-t^2, so he is accelerating down the hill).

ekt_bear: Sometimes a picture speaks more clearly than words do:

The blue line is Monday. The green line is Tuesday.

No matter how you choose the velocities, his position is bound to intersect.

(In this plot I chose x(t) = t, so constant speed on Monday. For Tuesday, y(t) = 1-t^2, so he is accelerating down the hill).

Lmao... Can you provide the intersection point, bro?