Burnt Candles

Algebra Level 3

I have 2 candles of the same length but different burning rates: one burnt in 4 hours and the other in 5 hours. Initially lighting at the same time, the lights are on for some time before being put out, and the physical length of one candle 4 times as long as than the physical length of the other.

How long in minutes have the candles been burning for?

The answer is 225.

1 solution

Soumava Pal
Feb 16, 2016

Let the lengths of the candles be 1 each.
We can assume the length to be 1 without loss of generality because it is only a matter of scaling. And let them burn for t hours each. In t hours the first candle burns $t/5$ and the second candle burns $t/4$ units. Therefore, $1-t/5$ =4(1-t/4) Solving this we will get t= $15/4$ hours which is 225 minutes.

It should be made more clear that the problem compares the remaining lenghts of the candles and not the remaining burning times!

Giuliano Bianco - 5 years, 3 months ago

220 minutes which = 3 hours and 40 minutes.

Meaning the remainder of the smaller rope is 20 minutes.

The remainder of the longer rope is 1 hour 20 minutes (or 80 minutes).

If it were 225 minutes, then the smaller rope would be 15 minutes whereas the longer rope would be 75 minutes, which is 5 times longer, not 4 times longer.

Phillip Foltz - 5 years, 3 months ago

Could you please point out what mistake I have done in the above solution?

Soumava Pal - 5 years, 3 months ago

I got 220 also. If we convert the burn time to minutes we get 240 for 4 hours. We get 300 minutes for 5 hours. Now we subtract x minutes from each. 240-x, and 300-x. Since the 5 hour candle will always be bigger than the other one, that is the the candle that is 4 times bigger after the x minutes of burning. So we have 300-x=4 (240-x). That becomes 300-x = 960-4x. That becomes 3x=660. Solve for x, and x=220. So it burns for 220 minutes.

Keven Anderson - 5 years, 3 months ago

@Keven Anderson – I believe that just gives you how much longer it takes to burn not length. In your calculation it takes one candle 4 times longer for the remainder of the candle to burn.

Brandon Rucker - 5 years, 3 months ago

75 minutes of the slow burning candle is four times the physical length of 15 minutes of the fast burning candle

Kevan St. John - 5 years, 3 months ago

Agreed I also got 220.

Jace Young - 5 years, 3 months ago

I think your solution is fine. After 225 minutes, the first candle with have 1/4 of its length remaining. The second candle will have 1/16 of its length remaining. Then the first candle will be four times as long as the second candle.

Brandon Rucker - 5 years, 3 months ago

Great! Glad to know! :)

Soumava Pal - 5 years, 3 months ago

Burnt Candles

The answer is 225.

1 solution

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