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This problem trains for: SAT-I, AMC-8, GMAT, Math Kangaroo 5-6, Math Kangaroo 7-8.

A glass jar is placed upside down over a burning red candle. After 3 minutes, the candle consumes all the oxygen in the jar and the burning stops. The same experiment is repeated after placing a green candle beside the red one. Burning simultaneously, the two candles consume the oxygen in the jar in 1.8 minutes. How many minutes does it take for the green candle alone to use up the oxygen in the jar?

The rate at which each of the candles consumes oxygen by burning is specific to the candle (i.e. may not be the same for both candles) but is the same during all experiments.

Denote the amount of oxygen in the jar by C.

Denote the rate at which the red candle burns oxygen by R.

Denote the rate at which the green candle burns oxygen by G.

Then, we can derive the amount of oxygen in two different ways, based on the two experiments:

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We can solve for the rate of the green candle:

equation

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The time needed by the green candle alone is obtained by dividing the amount of oxygen C by the rate at which it burns G:

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and we can express both quantities in terms of R:

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