Two candles of the same height are lit at the same time. The first is consumed in 4 hours, the second in 3...?

Question

hours. Assuming that each candle burns at a constant rate, how many hours after being lit was the first candle twice the height of the second?

Please show your work =) thx

Answer 1

Showing work requires CONSTANTS. In your first sentence, you claim that the candles are the same height. In the third sentence, you claim to have "the first candle twice the height of the second."

Are there two candles, or three? How many candles are the same height of the first candle? Should we assume that all other candles are the same width (diameter) or of the same composition?

This question is not complete. There is not enough accurate information to show work.

Answer 2

Let h be the height of the candle

speed of First Candle = h/4
speed of Second Candle = h/3

how many hours after being lit was the first candle twice the height of the second?

let r be the height of the second candle at that time (t).
r = h - (h/3)t

at the same time(t), the height of the first candle must be 2r
2r = h - (h/4)t

2(h-(h/3)t) = h - (h/4)t
2h - (2/3)ht = h - (1/4)ht
2-(2/3)t = 1 - (1/4)t
t(2/3-1/4) = 1
t = 12/5 hr or 2.4 hr

Answer 3

Dear lovable Heart of GOLD!
I think u failed to intuitively feel that the candles are not of the same diameter.Difference in diameter is the reason for the difference in time.
let the length of the candles initially be L m.
For the first candle, L m is burnt in 4 hrs.So,in 1 hr,(L/4)th of the candle is burnt.
For the second candle, L m is burnt in 4 hrs.So,in 1 hr,(L/3)rd of the candle is burnt.
Lets assume in X hrs the first candle's height is twice that of the second.
So,in X hours, the height of the first candle is =L(1-X/4)
So,in X hours, the height of the second candle is =L(1-X/3)

Equating for the given condition,that is,first candle's height is twice that of the second, we get

---> L(1-X/4)=2*L(1-X/3)
X=2.4 hrs
Ans: 2.4 hours...

Answer 4

the version between the time that the two candles are lit is two hours. 2hrs out of 6 hrs = 2/6 6 - 2 = 4 instruments so candle A(the single lit at 6 pm) is left with 4 instruments while candle B starts to burn at 8 pm. At 9, Candle a is left with 3 instruments mutually as candle B is left with 6 instruments. At 10 pm, candle A is left with 2 instruments mutually as candle B is left with 4. Gotcha! So the time is 10 pm.

Answer 5

Let the height of both the candles be x units. The first candle burns at x/4 units per hour and the second burns at x/3 units per hour.

Let the given condition be satisfied after h hours.

Height of the first after h hours = x-xh/4
Height of the second after h hours = x-xh/3

Height of first = 2 (height of second)
(x-xh/4) = 2 (x- xh/3)

3(4x-xh) = 8 (3x-xh)

eliminating x as x not =0

3(4-h) = 8 (3-h)

-3h+8h = 24-12

5h = 12

h = 12/5 hrs, i.e. 2 hours and 24 min.(2/5*60)

Answer 6

let the length of the candle1 =L1
length of candle2 =L2

the lengths of the candles can be expressed as a function of time(T)

Let the original length of the candle be 1.

L1 = 1-(1/4)T
L2 =1 -(1/3)T

L1 =2*L2

now substitute the formulas(with T as the function) into the equation.

Solve for T.

Answer 7

Most candle are tapered which would slow down the length of candle burned each hour.There fore it can't be calculated with out the top and bottom diameters of the candles.

Answer 8

heat from the first candle makes the second candle burn faster than the first candle

Answer 9

As is does not matter what size the candles are it will help you to make that size visible. Both start at 100% of their size.

1st candle burns at 25% per hour. 2nd at 33.33% per hour.

When C2 (candle 2) is at half it's size 90 minutes have passed.
in that time C1 came down 37.5%. 62.5% is left.

To get C2 to 33.33% (about half what C1 was) 2 hours (120 minutes)
C1 is at 50% at that time.

Getting closer.....

Uh......repeating this is not math....but it will get you there.

Answer 10

i can't show my work, but i can say that this has happened to me so many times and i DO NOT for the life of me understand WHY the candles burn differently!