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A red candle is 8 inches tall and burns at a rate of 7/10 inch per hour. A blue candle is 6 inches tall and burns at a rate of 1/5 inch per hour. After how many hours will both candles be the same height?


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Respuesta :

Answer: After 4 hours both candles be at the same height .

Explanation:

Since we have given that

Height of red candle = 8 inches

Rate at which red candle is burning is given by

[tex]\frac{7}{10}\ inch\ per\ hour[/tex]

Height of blue candle = 6 inches

Rate at which blue candle is burning is given by

[tex]\frac{1}{5}\ inch\ per\ hour[/tex]

Let 'y' be the height of both the candles after burning

Let 'x' be the amount of time it burns in hours.

So, equation for red candle be

[tex]y=8-\frac{7}{10}x[/tex]

equation for blue candle be

[tex]y=6-\frac{1}{5}x[/tex]

According to question, we get

[tex]8-\frac{7}{10}x=6-\frac{1}{5}x\\\\8-6=\frac{7}{10}x-\frac{1}{5}x\\\\2=\frac{7x-2x}{10}\\\\2=\frac{5x}{10}\\\\2=\frac{1x}{2}\\\\2\times 2=x\\\\4\ hours=x[/tex]

Hence, after 4 hours both candles be at the same height .


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