The worlds first riddle!

[size=7]Bottle Heating
In general
Q=mCpDelT
where DelT is temperature difference (100-T),
m is mass of bottle and contents
& Cp is heat capacity of bottle and contants
DelT=Q/mCp
At constant DelT ---Q is constant, but in this case T (& DelT) changes with respect to time (t)
so
dT/dt=d(Q/mCp)/dt=1/(mCp)dQ/dt
(m & Cp are constants)
dQ/dt=mCpdT/dt=mCpd(DelT)
m & Cp <>0
dT/dt=(DelT)=(100-T) in this cast
seperating variables
dT/(100-T)=dt
integrating
-ln(100-T)=t+K K is constant of integration
@ t=0 T=15 then
K=-ln(85)
-ln(100-T)=t-ln(85)
ln[85/(100-T)]=t
85/(100-T)=exp(t)
the function of bottle temperature T with respect to time (t) is
T=100-85exp(-t)
Solve for t @ T=25
25=100-85exp(-t)
85exp(-t)=75
exp(-t)=75/85=15/17
t=ln(17/15) min~=0.125 min=7.5 sec[/size]
Rap

Rap:

Bottle Heating
In general
Q=mCpDelT
where DelT is temperature difference (100-T),
m is mass of bottle and contents
& Cp is heat capacity of bottle and contants
DelT=Q/mCp
At constant DelT ---Q is constant, but in this case T (& DelT) changes with respect to time (t)
so
dT/dt=d(Q/mCp)/dt=1/(mCp)dQ/dt
(m & Cp are constants)
dQ/dt=mCpdT/dt=mCpd(DelT)
m & Cp <>0
dT/dt=(DelT)=(100-T) in this cast
seperating variables
dT/(100-T)=dt
integrating
-ln(100-T)=t+K K is constant of integration
@ t=0 T=15 then
K=-ln(85)
-ln(100-T)=t-ln(85)
ln[85/(100-T)]=t
85/(100-T)=exp(t)
the function of bottle temperature T with respect to time (t) is
T=100-85exp(-t)
Solve for t @ T=25
25=100-85exp(-t)
85exp(-t)=75
exp(-t)=75/85=15/17
t=ln(17/15) min~=0.125 min=7.5 sec


Thank you Rap, that has made my day. A better answer would be impossible to find!

A variation on an old theme:


You are traveling down a path and come to a fork in the road. A sign lays fallen at the path indicating that one path leads to a village where everyone tells the truth and the other to a village where everyone tells lies.

The sign has been knocked down so you do not know which path leads to which village. Then someone from one of the villages (you don't know which one) comes down the path.

You may ask him one question to determine which path goes to which village.

What ONE question do you ask

VARIATION
[size=7]Which way would a member of the other village say leads to the village where everyone tells lies?

His answer will indicate the direction of the village where everyone tells the truth.[/size]

[size=7]Which village did you come from?
Go that way to the truth village, the other way to the lying village--but first put the sign back up.

Reason
If they came from the lying village they point to the truth village. If they came from the truth village thay point to the truth village.[/size]

Rap

I like rap's - short and sweet.

Mark:

VARIATION

Which way would a member of the other village say leads to the village where everyone tells lies?

His answer will indicate the direction of the village where everyone tells the truth.


Rap:

Which village did you come from?

Go that way to the truth village, the other way to the lying village--but first put the sign back up.

Reason
If they came from the lying village they point to the truth village. If they came from the truth village thay point to the truth village.



Before you choose the answer you like best; consider these four questions:

1. If you point to the truthful village what will a truthful person say in answer to your question?

2. If you point to the truthful village what will a untruthful person say in answer to your question?

3. If you point to the untruthful village what will a truthful person say in answer to your question?

4. If you point to the untruthful village what will a untruthful person say in answer to your question?

The answers to these questions are: 1. "yes", 2. "yes", 3. "no", 4. "no".

Note that in the two cases where the answer is "yes" you are pointing to the truthful village and in the two cases where the answer is "no" you are pointing to the untruthful village. Thus you can tell from the reply to which village you are pointing. You do not have to know to whom you are speaking.



Answer 1: Say, "Please point to the village you are from." Regardless of where they are from they will point to the truthful village.

Answer 2: You point to either path and say, "Are you from this village?" If the person answers 'yes' then you are pointing to the truthful village, if they answer 'no' then you are pointing to the lying village.

Answer 3: Ask "Which path would a person from the other village say leads to the truthful (or untruthful) village?" Regardless of whom you speak to the answer will filter through one lie, so if you ask for the truthful village the person will point to the lying village, and visa versa.


"I like rap's - short and sweet."

Rap's short and sweet; what!




VITPARATITYON

VITPARATITYON= party invitation

Stormy:

VITPARATITYON= party invitation


I hope you have received yours!



DFS

DWOWS

FINDS

WINDOWS

No, I never get invited!

Arabian Nights On The Ship - formally invited
NewChezIzzie House Warming Party - formally invited

CTCHG

MTS

it's all about timing a?

mints (chocolate sounds good)


Hey thoh, mark, raprap and any other riddler, a post from each of you is being requested on this thread. Don't want you to get lost, so here:
http://www.able2know.org/forums/viewtopic.php?t=111721&start=1220&postdays=0&postorder=asc&highlight=


btw just a hi will do

Posted: Mon Mar 10, 2008 7:31 am

DFS

DWOWS


Lzzie: Posted: Mon Mar 10, 2008 7:34 am

FINDS

WINDOWS

Three freekin minutes; what kept you, did you have to finish painting a fence!



There is a 6 foot wide alley. Both walls of the alley are perpendicular to the ground. Two ladders, one 10 feet long, the other 12 feet, are propped up from opposite corners to the adjacent wall, forming an X shape.

All four feet of each ladder are firmly touching either the corner or the wall. The two ladders are also touching each other at the intersection of the X shape.

What is the distance from the point of intersection to the ground

GUESS YOU DIDN'T GET MINE 'HUH - gosh, how quick do ya need to be a? :wink:

[size=7]Complete the triangles
the 10 ft ladder is 6:8:10
the 12 ft ladder is 6:6*3^.5:12
at intersection the triangles create to similar triangles to ladders
the height of both triangles is d, the bases are r and (6-r)
since triangles are similar to ladders on is
r/d=6/(6*3^.5)
rearranging
r=d/3^.5
the other is
(6-r)/d=8/6
r=(18-4d)/3
equate
d/3^.3=(18-4d)/3
solve for d
d=18*3^.5/(3+4*3^.5)
this is messy
working through some tedious arithmetic
d=(4+3^.5)/5 ft[/size]

Rap

Some puzzles for the late night crowd:

QUIMSIITNIDVSE

TEDRIELSETMIMNAG

SNOERMVNOIUSA

INQUISITIVE MINDS

(oh thanku Stormy - keeping me busy girl)

INTERESTING DILEMMA