How Long Are The Candles - Answer

(Solution Hidden)


This post presents the solution to the puzzle "How Long are the Candles?"

The first thing to notice is that, at 9pm, the candles are the same length. At this point, it takes the longer candle 2 hours to burn away, but it only takes the shorter candle 1.5 hours. This means that the candles do not burn at the same rate.

I made myself the following diagram:

y+1 y
6 4

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x x
2 1.5

This diagram shows the two candles, and divides them into two parts.

The bottom part is the length of the two candles at 9pm (when they were equal - call it x inches), as well as the number of hours it took each candle to burn that length. So, the longer candle burned at a rate (r1) equal to x/2, and the shorter candle burned at a rate (r2) of x/1.5.

The top part is the length of the two candles that burned up by 9pm, as well as the number of hours it took each candle to burn that length. So, the longer candle burned at a rate (r1) equal to(y+1)/6, and the shorter candle burned at a rate (r2) of y/4.


We now have two equations with 2 unknowns:

r1 = r1
x/2 = (y+1)/6
2y+2 = 6x

r2 = r2
x/1.5 = y/4
4x = 1.5y
x = 1.5y/4

If we now plug the second equation into the first, we get

2y+2 = 6*1.5y/4
2y+2 = 9y/4
2 = 9y/4 - 2y
2 = 9y/4 - 8y/4
2 = y/4
8 = y

We then get x = 1.5(8)/4 = 3

So, the longer candle is x + y +1 = 12 inches.

The shorter candle is x + y = 11 inches.

How Long Are The Candles?

This is from the 12/16/2007 "Ask Marilyn" column in Parade magazine:

I have two candles, one an inch longer than the other. I light the longer one at 3 pm and the shorter one at 5 pm.

At 9 pm, they're the same length.

The longer candle goes out at 11 pm, and the shorter one goes out at 10:30 pm.

How long were they at the start?

Please click here for the answer.

Timing With Hourglasses - the Answer

(Solution Hidden)



1. Start both hourglasses when you grab the first little piggy.

2. When the 7-minute glass runs out, turn it over.

3. When the 11-minute hourglass runs out, turn the 7-minute glass again.

At this point, 11 minutes have passed and 4 minutes remain in the 7-minute hourglass.

4. When the 7-minute glass runs out, 15 minutes have passed.

Timing With Hourglasses

This is also from the AskMarilyn column in the December 2, 2007 Parade Magazine:

Your rich uncle dies, and you're in his will. From his collection of timepieces, he leaves you the 7-minute hourglass and the 11-minute hourglass.

To honor his memory, you open a reflexology salon and use the hourglasses when you give foot massages. But your clients want 15-minute massages instead.

How do you use your cherished timepieces and still manage to please your clients?

Please click here for the answer.

Which Word Does Not Belong? - Answer

(Solution Hidden)



Refrigerator does not belong.

All 6 words have a short form, but only refrigerator has a short form that is not made up of the first few letters.

advertisement = ad

automobile = auto

condominium = condo

gymnasium = gym

refrigerator = fridge

veterinarian = vet

Which Word Does Not Belong?

This is from the AskMarilyn column in the December 2, 2007 Parade Magazine:

Which of the following words does not belong:

advertisement

automobile

condominium

gymnasium

refrigerator

veterinarian


Please click here for the answer.