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 h

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 hight?

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Kiệt Gia 5 months 2021-08-14T01:35:18+00:00 1 Answers 454 views 0

Answers ( )

    1
    2021-08-14T01:37:13+00:00

    Answer:

    4 hours

    Step-by-step explanation:

    Given that:

    Initial height of red candle = 8 inches

    Rate of burning of red candle = \frac{7}{10}\ inch/hr

    Initial height of blue candle = 6 inches

    Rate of burning of blue candle = \frac{1}{5}\ inch/hr

    To find:

    Time taken in hours such that both the candles have the same height.

    Solution:

    Let the time taken such that both the candles have the same height = t hours

    Height of red candle after t hours = (8 - \frac{7}{10}t) \ inches

    Height of blue candle after t hours = (6 - \frac{1}{5}t) \ inches

    Writing both the expressions as equal:

    8-\dfrac{7}{10}t=6-\dfrac{1}{5}t\\\Rightarrow 8-6=\dfrac{7}{10}-\dfrac{1}{5}t\\\Rightarrow 2 = (\dfrac{7-2}{10})t\\\Rightarrow \dfrac{5t}{10}=2\\\Rightarrow t=4\ hours

    After 4 hours, height of both the candles will be same.

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