A candle weighs 12 oz. It burns for 5 hrs and 0.8 oz are....

mhb1959

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A friend and I are getting different answers for the same problem. I would like to know which method for solving is correct, and why the other one does not work.

The Problem:

A candle weighs 12 oz.
It burns for 5 hours and .8 oz are consumed.
How long will it take for the remainder of the candle to burn?

I set up my formula this way:

(12 / 12) - (.8 / 12) = (11.2 / 12), or .94, that's how much candle you still have left

therefore, .06 is the percentage which burned in 5 hours

so you set up a purportional equation

(5 hrs./ .06) = (x / .94), where x = how long it will take the remainder to burn, assuming the same rate

5 hrs. /.06 * .94 = x

78.333 hrs. = x

==================

My friend figures it this way:

Total estimated burn time = (initial mass)(duration of test burn)/(change in mass)

so,

(12 oz)(5 hours) = 60 divided by .8 = 75

[/u]
 

galactus

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\(\displaystyle \L\\\frac{x+5}{12}=\frac{5}{0.8}\)

x=70 hrs for the rest of the candle to burn.
 

Subhotosh Khan

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Both methods are correct - the problem is in execution.

You have a problem of rounding 0.8/12 = 0.0667

The remainder is then 0.9333

Now

x = 5 * 0.9333/0.0667 = 69.96

If you left everything in fraction - the answer would be a nice and even 70.

Your friend calculated the time to burn the whole candle (not remainder - as asked). He would get a 100% if he had subtracted 5 (the time to burn the initial part) from his answer.
 

TchrWill

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A candle weighs 12 oz.
It burns for 5 hours and .8 oz are consumed.
How long will it take for the remainder of the candle to burn?

If it tkes 5 hr to burn 8 oz., it will take x hr to burn 12 oz., or 5/8 = x/12 or x = 7.5 hr.

Therefore, it will take 7.5 - 5 = 2.5 hr to burn the remainder of the candle.
 

Subhotosh Khan

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TchrWill said:
A candle weighs 12 oz.
It burns for 5 hours and .8 oz are consumed.

If it tkes 5 hr to burn 8 oz ., ......
TchrWill,

In 5 hours it burnt 0.8 oz - not 8 oz.
 

TchrWill

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My most humble apologies. This will teach me to wait for the effects of my eye injection to wear off before I tackle any problems. I completely missed the decimal point as in .8 oz. as opposed to 8 oz. which I assumed I was reading.

Clearly, the burn time remaining derives from

5/.8 = x/12 making x = 75 and the remaining burn time is 75 - 5 = 70 ours.
 

stapel

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TchrWill said:
This will teach me to wait for the effects of my eye injection to wear off before I tackle any problems....
Ouch! You're getting stuff injected into your eye?!? :shock:

By the way, I nearly missed the decimal point, too. My only excuse, I supposed, is age and bifocals, but the confusion does point up the need for clarity: "0.8" is so much easier to "see" than is ".8"! :D

Eliz.
 

galactus

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That's why it should be written as 0.8
 
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