Two candles of the same height are lighted at the same time.

Question

Two candles of the same height are lighted at the same time. The first candle is consumed in 4 hours and the second one in 3 hours. Assume that each candle burns at the same rate. In how many hours will the first candle measure twice the height of the second candle?

(A) 1 hour and 12 minutes

(B) 2 hours and 24 minutes

(C) 3 hours and 45 minutes

(D) 4 hours and 10 minutes

(E) 4 hours and 48 minute

(A) 1 hour and 12 minutes

(B) 2 hours and 24 minutes

(C) 3 hours and 45 minutes

(D) 4 hours and 10 minutes

(E) 4 hours and 48 minutes

Fdambro294 · Accepted Answer

the question is supposed to say "each candle burns at a CONSTANT rate", not the Same Rate....

I've been scratching my head for 5 minutes.

ScottTargetTestPrep · Answer

We can let the height of both candles be 12 inches. So the first candle burns at a rate of 3 inches per hour and the second candle at a rate of 4 inches per hour. We can let x = the number of hours it takes the first candle to be twice the height of the second candle.

12 - 3x = 2(12 - 4x)

12 - 3x = 24 - 8x

5x = 12

x = 2.4 hours = 2 hours 24 minutes
 
Answer: B

nick1816 · Answer

After any given time(t), length of first candle=  L-\frac{Lt}{4} 
After any given time(t), length of second candle=  L-\frac{Lt}{3}

Time(t) after the first candle measure twice the height of the second candle

L-\frac{Lt}{4} = 2* L-\frac{Lt}{3}] 
 1-\frac{t}{4}=2-\frac{2t}{3} 
 \frac{2t}{3}-\frac{t}{4}=1 
 \frac{8t-3t}{12}=1 
5t=12
t=2.4 hours = 2 hours and 24 minutes

AhmadAli250 · Answer

Let, h0=initial height of both candles, t=initial time of burning of both candles, h1=current height of first candle, h2=current height of second candle

=> h1=h0-(h0*t)/4; h2=h0-(h0*t)/3. Putting these eqs in h1=2*h2
=> 1-t/4 = 2(1-t/3)
=> t=12/5 h = 2.4 h = 2h and 24min

gmathack93 · Answer

Can somebody help me explain what is Lt/4 and respectively Lt/3 in the above solution.

The solution seems elegent. However, I am not able to fit the in term of RT=W relationation.

Thx in advance !!

Fantasy_app · Answer

Let the height of each candle be L ( as they have the same height)
then, 
Rate of burning for first candle will be = L/4 (as it burns completely in 4 hours) 
Rate of burning for second candle will be = L/3 (completely burns in 3 hours)

Therefore, after time 't'
the height of the first candle burned = L/4 * t       <----- (rate * time)
and the height of the second candle burned = L/3 * t

Height of first candle remaining after time 't' = L-Lt/4 -----(i)
Height of second candle remaining after time 't' = L-Lt/3 -----(ii)

Now we know, (i) = 2 * (ii)
Upon calculation, we get t= 2 hours 24 minutes.

Hope that helps!

Fantasy_app · Answer

Let the height of each candle be L ( as they have the same height)
then, 
Rate of burning for first candle will be = L/4 (as it burns completely in 4 hours) 
Rate of burning for second candle will be = L/3 (completely burns in 3 hours)

Therefore, after time 't'
the height of the first candle burned = L/4 * t       <----- (rate * time)
and the height of the second candle burned = L/3 * t

Height of first candle remaining after time 't' = L-Lt/4 -----(i)
Height of second candle remaining after time 't' = L-Lt/3 -----(ii)

Now we know, (i) = 2 * (ii)
Upon calculation, we get t= 2 hours 24 minutes.

Hope that helps!

bundela.ajay · Answer

same, i was so confused when the question said, they had the same height and were burning at the same rate, but took different time lol

bobojonovo16 · Answer

Thе answers C D E dont make sense because one of the candles are gonna be burned up till that time. We are only left with A and B. If we conider A the rate at which the candles do not allow it to happen because the rates are not that much different. The only logical answer is B based on the intuition and logic.

bumpbot · Answer

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Two candles of the same height are lighted at the same time.

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