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Lucario621 wrote:

There are two candles of equal height. One will burn for 4 hours, the other will burn for 5 hours. They are each lit at midnight. Assuming each candle burns at a constant rate, at what time will one candle be 4 times the height of the other candle?

This is not a trick question. Can somebody help me figure it out? Its a problem of day at math class, and because its hard, my teacher is letting it stay up for a couple of days. Can you help me figure it out?

One of my ideas was to make generally a graph/Cartesian plane, in which x is the amount of time, and y is the height. We start out at any height, it doesn't matter, so I decided to do 60 inches. I drew one line strait from the 60 in mark to the 4 hr mark, and I drew one strait from the 60 in mark to the 5 hr mark. The I looked for the point at which the 4 hr line is 1/4 of the size of the 5 hr line. Thats the point. So its about 3:45, yes? But the thing is, using this method, we can't tell the exact time, by minute and second.

Please help!

Assume Height = 300, for an easy number's sake.
Candle A will burn 75 each hour for 4 hours. Candle B will burn 60 each hour for 5 hours.
0 hours = 300/300
1 Hour = 225 / 240
2 hours = 150 / 180
3 hours = 75 / 120
3.5 hours = 37.5 / 90
3.6 hours = 30 / 84
3.7 = 22.5 / 78
3.8 = 15 / 72

Through trial and error, it has to be somewhere between 3.7 and 3.8

3.75 hours = 18.75 / 75   <---------- 18.75 is exactly one quarter of 75.
If the candle started burning at midnight, then one candle would be 4 times the height of the other 3.75 hours after.
So at 3.45 in the morning, I think. There's your answer.
You don't need hugely advanced mathematics to work out some problems. 

djm111 wrote:

Lucario621 wrote:

There are two candles of equal height. One will burn for 4 hours, the other will burn for 5 hours. They are each lit at midnight. Assuming each candle burns at a constant rate, at what time will one candle be 4 times the height of the other candle?

This is not a trick question. Can somebody help me figure it out? Its a problem of day at math class, and because its hard, my teacher is letting it stay up for a couple of days. Can you help me figure it out?

One of my ideas was to make generally a graph/Cartesian plane, in which x is the amount of time, and y is the height. We start out at any height, it doesn't matter, so I decided to do 60 inches. I drew one line strait from the 60 in mark to the 4 hr mark, and I drew one strait from the 60 in mark to the 5 hr mark. The I looked for the point at which the 4 hr line is 1/4 of the size of the 5 hr line. Thats the point. So its about 3:45, yes? But the thing is, using this method, we can't tell the exact time, by minute and second.

Please help!

Assume Height = 300, for an easy number's sake.
Candle A will burn 75 each hour for 4 hours. Candle B will burn 60 each hour for 5 hours.
0 hours = 300/300
1 Hour = 225 / 240
2 hours = 150 / 180
3 hours = 75 / 120
3.5 hours = 37.5 / 90
3.6 hours = 30 / 84
3.7 = 22.5 / 78
3.8 = 15 / 72

Through trial and error, it has to be somewhere between 3.7 and 3.8

3.75 hours = 18.75 / 75   <---------- 18.75 is exactly one quarter of 75.
If the candle started burning at midnight, then one candle would be 4 times the height of the other 3.75 hours after.
So at 3.45 in the morning, I think. There's your answer.
You don't need hugely advanced mathematics to work out some problems. 

Oh thanks ^^