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Two candles have the same length but they are made of different materials. One of these candles burn completely in 3 hours and the other burn completely in 4 hour. Both of the candles burn in a uniform rate.

 

At what time should I lit both candles if I want that the length of one candle be twice the length of the other candle exactly at 4:00 pm?

 Jan 5, 2020
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rate x time = distance     (or amount burned away)

 

1 candle / 3hr   = 1/3 candle/ hr   for rate of the fast burner    the other is 1/4 candle/hr

The amount of candle remaining after some time t   is   1 candle - rate* t

The slower burner will be twice as long as the faster burner at what point?

 

1 - 1/4 candle/ hr  x t     = (1   - 1/3 candle/hr x t)  x 2      solve for t

 

1-1/4 t = 2 - 2/3 t

-3/12 t = 1 - 8/12 t

5/12 t = 1

t = 12/5 = 2.4 hours           start 2.4 hours before 4 pm      or   1:36 PM

 Jan 5, 2020
edited by ElectricPavlov  Jan 5, 2020

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