Two candles and time?

Two candles of equal length are lighted at noon. One candle takes 9 hours to burn out, and the other takes 6 hours to burn out. At what time will the slower-burning candle be exactly twice as long as the faster-burning one?

I’ve tried to determine their ‘work rate’ and multiply it by ‘x’ time, but it did not work for me. Could somebody show me the light? Thanks!

Top 1 Answers

A few days ago

Anonymous

Favorite Answer

Candle A takes 9hr. to burn out. Therefore 1/9 of its length burns each hour.

Candle B takes 6hr. Therefore 1/6 of its length burns each hour.

The fraction of candle A which is left after t hours is 1 – (t/9), and the fraction of candle B left is 1 – (t/6).

Therefore if t hours is the required time:

1 – t/9 = 2(1 – t/6)

Multiplying by 9:

9 – t = 18 – 3t

2t = 9

t = 9/2.

The required time is 9/2 hr.

Check:

After 9/2hr, the fraction of A left is 1 – 1/2 = 1/2.

The fraction of B left is 1 – 9/(2*6) = 1/4.

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