We had a power outage Saturday Night (Car accident took at a regulator bank). Obviously I couldn't go online to the forums so I decided to read a book (Nero Wolfe - Trio for blunt instruments). Rather than using a flashlight… I lit a candle to provide light to read by. An hour and one-half later… the power still wasn't back on so I lit a second candle to provide more reading light. This second candle was an inch shorter than the original length of the first candle. Two and one-half hours later, I took a break to get a glass of milk and noticed that the candles were now the same length. Another hour and one-half later, just as I finished my book, the candle that started out shortest burned out. I left the original candle burning to provide a bit of light to get ready for bed by. The original candle burned out after half and hour.
What was the original length of each candle?
We had a power outage Saturday Night (Car accident took at a regulator bank). Obviously I couldn't go online to the forums so I decided to read a book (Nero Wolfe - Trio for blunt instruments). Rather than using a flashlight… I lit a candle to provide light to read by. An hour and one-half later… the power still wasn't back on so I lit a second candle to provide more reading light. This second candle was an inch shorter than the original length of the first candle. Two and one-half hours later, I took a break to get a glass of milk and noticed that the candles were now the same length. Another hour and one-half later, just as I finished my book, the candle that started out shortest burned out. I left the original candle burning to provide a bit of light to get ready for bed by. The original candle burned out after half and hour.
What was the original length of each candle?
ok my first guess,
3inches and 2 inches.
somethings not right tho, because i do not get them being the same length after both burning for 150 minutes, yet i know the second candle started off exactly 1 inch shorter than the first candles original length. so that must mean the first candle took 120mins to burn that 1 inch, because that's how much longer it was alight, 90 minutes at the beginning and 30 minutes at the end.
therefore original candle burned for a total of 360 minutes, meaning it must of been 3inches high, 2nd candle started off 1inch shorter so it was 2 inches high.
now this is were i get a problem after 240 mins(90 it was alight first + 150 since 2nd was lit) for the first candle it's 1 inch high but the second candle after the 150mins it's a quarter of and inch shorter.. so something is wrong with my calcs/logic(wouldn't surprise me) or the way the puzzle is worded.
mmmm
candle burned out after half and hour.
i took this to mean half an hour(30mins) but let me rework my calcs with it meaning an hour and half(90mins).
nope still can't get them to be exactly the same length after both burning for 150mins, but it would make them 2 and a 3rd inches and 1 and a 3rd inches to start with.
i'm beginning to wonder if they both burn at the same rate and even if the first candle started out at it's original length, maybe that to had been part used.
ok i know the answer but won't post it because i cheated, but i will give anyone trying to work it out a clue,
the candles do not burn at the same rate(my mistake) and is why they are the same length after 150 mins.
or
120mins burn time on 1st candle equals 90mins burn time on candle2 ie. when they were both the same length.
Jimbo1 – How are you! So nice to see you here!
Terry1969 – I've known you were Good for a very long time, now. And… I'm STILL right !!
otisx – HEY! Nice to see you again! I'm going to try to figure this out, too.
TomK – HEY TOMK!! Miss you. Your posts always make me smile.
O.K.
I'm going to try an "on-line work-in-progress approach".
Anyone can feel free to jump in at any time. It will appear as a series of posts – each chronologically depicting "solver's thought processes" – until we find an answer.
I'll begin below!
Let first and second candle have original length in inches X and Y respectively.
From
This second candle was an inch shorter than the original length of the first candle.
We get X - Y = 1 or X = Y + 1 —— (1)
From
Two and one-half hours later, I took a break to get a glass of milk and noticed that the candles were now the same length.
We get that each candle has diferent rate of burning.
We can express each rate mathematicaly assuming that rate at which candle burns is uniform.
By definition Uniform Rate = Original Length / Total time candle burns.
Rate for first candle is X / 6 inches per hour. (Since time candle burns is 6 hrs)
Rate for second candle is Y / 4 inches per hour. (Since time second candle burns is 4 hrs)
We know that at any given time the length of a candle is equal to Original Length minus Rate * Time Elapsed.
Since we know what time elapsed for each candle when length was the same, We get:
X - 4X/6 = Y - 3Y/8 ——– (2)
Solve the simultaneous equations (1) and (2) and we get:
nope wrong answer otisx but your thinking along the right lines..
x = length of candle 1, y = length of candle 2 or y = (x-1)
burn rate of candle 1 = b1
burn rate of candle 2 = b2
when they are both the same length after 240 minutes or 4 hrs burning for candle 1 and 150 minutes or 2.5 hrs for candle 2
x-4*b1 = y-2.5*b2
when they have both burned out
x=6*b1 and y=4*b2
that should help you work out the burn rate per hr for each candle and then the correct lengths…
Let first and second candle have original length in inches X and Y respectively.
From
This second candle was an inch shorter than the original length of the first candle.
We get X - Y = 1 or X = Y + 1 —— (1)
From
Two and one-half hours later, I took a break to get a glass of milk and noticed that the candles were now the same length.
We get that each candle has diferent rate of burning.
We can express each rate mathematicaly assuming that rate at which candle burns is uniform.
By definition Uniform Rate = Original Length / Total time candle burns.
Rate for first candle is X / 6 inches per hour. (Since time candle burns is 6 hrs)
Rate for second candle is Y / 4 inches per hour. (Since time second candle burns is 4 hrs)
We know that at any given time the length of a candle is equal to Original Length minus Rate * Time Elapsed.
Since we know what time elapsed for each candle when length was the same, We get:
X - 4X/6 = Y - 5Y/8 ——– (2)
Solve the simultaneous equations (1) and (2) and we get:
Hey everyone!
Just dropped in to say hello. I started my first uni unit 6 weeks ago and although it is nothing like I expected, I'm absolutely loving the challenge! Anxiously waiting for the results of my first assignment which are due back on Tuesday.
Anyway, going to go have a browse around, my head needs a break from the infinite research-read-write
Bye , have fun, and I will pop in again and might even have a crack at a Monday Madness someday soon!
I have not read any responses yet. I want to see if I can figure this out. I went to post last night and lost IE8 connection and all my work on the post. Sorry…
Here's a cc: that I sent to "Software" forums to see if I can at least retrieve my "Preview" which was successful.
and
Last night while answering Monday Madness, I spent thoughtful time creating thoughtful answer to submit of which I was very proud. I previewed my post, as per usual, and it looked good. I entered "Reply" to finalize post. Instead of showing me my finalized post, I was informed that my IE8 connection was lost. So were the connections for all household computers. (I'm on a PC, then there are 2 laptops which share connection.)
We were not able to connect until this morning after an "unplug and reboot" session.
Any chance my "previewed" post is stored somewhere that it could be retrieved?
Everytime I create a thoughtful post which requires time to create on the forum, it always gets lost. It seems to happen mostly when it takes me time to compose a thoughtful answer. Is this usual? What can I do about this?
Jimbo1
Just dropped in to say hello. I started my first uni unit 6 weeks ago and although it is nothing like I expected, I'm absolutely loving the challenge! Anxiously waiting for the results of my first assignment which are due back on Tuesday. 
Anyway, going to go have a browse around, my head needs a break from the infinite research-read-write 
Bye 
, have fun, and I will pop in again and might even have a crack at a Monday Madness someday soon! 
and 
Last night while answering Monday Madness, I spent thoughtful time creating thoughtful answer to submit of which I was very proud. I previewed my post, as per usual, and it looked good. I entered "Reply" to finalize post. Instead of showing me my finalized post, I was informed that my IE8 connection was lost. So were the connections for all household computers. (I'm on a PC, then there are 2 laptops which share connection.)
We were not able to connect until this morning after an "unplug and reboot" session.
Any chance my "previewed" post is stored somewhere that it could be retrieved?
Everytime I create a thoughtful post which requires time to create on the forum, it always gets lost. It seems to happen mostly when it takes me time to compose a thoughtful answer. Is this usual? What can I do about this?
