Time with Candles

Algebra Level 1

To keep track of time, an adventurer carries two cylindrical candles of equal heights but different radii. One takes 6 hours and the other takes 9 hours to burn out.

Now, the adventurer lights both candles and goes to sleep. If one candle is twice the height of the other when he wakes up, how much time has he slept?

4 hours and 30 minutes 5 hours 5 hours and 30 minutes 6 hours

2 solutions

Marta Reece
Jul 28, 2017

Length of candle 1 as a function of time is $y_1=L-\frac L6t$ where $L$ is the starting length.

Length of candle 2 is $y_2=L-\frac L9t$

If $y_2=2y_1$ , then $L-\frac L9t=2(L-\frac L6t)$

With solution $t=\frac92$ which corresponds to time $\boxed{4:30}$

Very nice explanation

Steve Smith - 1 year, 5 months ago

James Moors
Jul 29, 2017

You could argue that any time after 9:00 would also be correct.

If both candles are of height zero, then technically "one candle is twice the height of the other". The other is also twice the height of the first.

he wakes up when one of the two candle is half as high as the other. The question is how much does he sleep, you can't say he slept 9 hours.

maxime weill - 3 years, 10 months ago

Why not? If he wakes up somewhere after 9 hrs, the condition still holds.

Divyayan Dey - 2 years, 3 months ago

If the height is zero, then there will be no candle and the adventurer will not even try to light the candle. The adventurer is sensible than you. So do not send such expiation again.

Steve Smith - 1 year, 5 months ago

Time with Candles

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