Two candles start burning at the same time. One candle is 15cm tall and burns at a rate of 5cm every 6 hours. The other candle is 25cm tall and burns at a rate of 2(1)/(2)cm every hour. How tall will the candles be when they first burn down to the same height? cm

Question

Two candles start burning at the same time. One candle is  15cm tall and burns at a rate of  5cm every 6 hours. The other candle is  25cm tall and burns at a rate of  2(1)/(2)cm every hour. How tall will the candles be when they first burn down to the same height?  cm

Bytelearn · Accepted Answer

Determine burn rates: Determine the burn rates of both candles. The first candle burns at a rate of 5 cm every 6 hours, which is equivalent to 5/6 cm per hour. The second candle burns at a rate of 2.5 cm every hour.Set up equation: Set up an equation to represent the height of each candle as a function of time. Let h1(t) be the height of the first candle at time t, and h2(t) be the height of the second candle at time t. h1(t) = 15 - (5/6)t h2(t) = 25 - 2.5tFind same height time: Find the time when both candles are the same height. Set h1(t) equal to h2(t) and solve for t. 15 - (5/6)t = 25 - 2.5tSolve for t: Solve the equation for t. Multiply both sides of the equation by 6 to clear the fraction: 6(15) - 5t = 6(25) - 15t 90 - 5t = 150 - 15tBring terms together: Bring the terms involving t to one side and constant terms to the other side. 90 - 150 = -15t + 5t -60 = -10tDivide to solve t: Divide both sides by -10 to solve for t. t = -60 / -10 t = 6 hoursCalculate height after 6 hours: Calculate the height of the candles after 6 hours. Substitute t = 6 into either h1(t) or h2(t). Using h1(t): h1(6) = 15 - (5/6)*6 h1(6) = 15 - 5 h1(6) = 10 cmVerify with second candle: Verify the height with the second candle's equation. Using h2(t): h2(6) = 25 - 2.5*6 h2(6) = 25 - 15 h2(6) = 10 cm

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