Question

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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Answer 1

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

Step-by-step explanation:

Since we have given that

Height of red candle = 8 inches

Rate at which red candle is burning is given by

`(7)/(10)\ inch\ per\ hour`

Height of blue candle = 6 inches

Rate at which blue candle is burning is given by

`(1)/(5)\ inch\ per\ hour`

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

`y=8-(7)/(10)x`

equation for blue candle be

`y=6-(1)/(5)x`

According to question, we get

`8-(7)/(10)x=6-(1)/(5)x\\\\8-6=(7)/(10)x-(1)/(5)x\\\\2=(7x-2x)/(10)\\\\2=(5x)/(10)\\\\2=(1x)/(2)\\\\2* 2=x\\\\4\ hours=x`

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