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

Calculate Candle Burning Rates: First candle burns 5cm every 6 hours, so it burns at a rate of 5cm / 6 hours = 5/6 cm per hour.Set Up Height Equations: Second candle burns 2(1)/(2)cm every hour, which is 2.5cm per hour.Find Time When Candles are Same Height: Let's call the time it takes for the candles to be the same height ＂t＂ hours. We can set up equations for the heights of the candles as they burn. First candle's height after t hours: 15 - (5/6)t Second candle's height after t hours: 25 - 2.5tSolve for Time: We want to find the time t when both candles are the same height, so we set the equations equal to each other: 15 - (5/6)t = 25 - 2.5tCalculate Height When Candles are Same: To solve for t, we'll first get rid of the fractions by multiplying everything by 6: 6(15) - 5t = 6(25) - 15tNow we simplify: 90 - 5t = 150 - 15tAdd 15t to both sides and subtract 90 from both sides: 10t = 60Divide both sides by 10 to solve for t: t = 60 / 10 t = 6 hoursNow we'll plug t back into one of the original height equations to find the height of the candles when they're the same. Let's use the first candle's equation: Height = 15 - (5/6)(6)Simplify the calculation: Height = 15 - 5 Height = 10 cm

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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

Two candles start burning at the same time. One candle is $15\,\text{cm}$ tall and burns at a rate of $5\,\text{cm}$ every $6$ hours. The other candle is $25\,\text{cm}$ tall and burns at a rate of $2\frac{1}{2}\,\text{cm}$ every hour. How tall will the candles be when they first burn down to the same height? $\newline$ $\square\,\text{cm}$

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Q. Two candles start burning at the same time. One candle is

15\,\text{cm}

tall and burns at a rate of

5\,\text{cm}

every

6

hours. The other candle is

25\,\text{cm}

tall and burns at a rate of

2\frac{1}{2}\,\text{cm}

every hour. How tall will the candles be when they first burn down to the same height?

\newline

\square\,\text{cm}

Calculate Candle Burning Rates: First candle burns $5\,\text{cm}$ every $6$ hours, so it burns at a rate of $\frac{5\,\text{cm}}{6\,\text{hours}} = \frac{5}{6}\,\text{cm}$ per hour.
Set Up Height Equations: Second candle burns $2\left(\frac{1}{2}\right)\text{cm}$ every hour, which is $2.5\text{cm}$ per hour.
Find Time When Candles are Same Height: Let's call the time it takes for the candles to be the same height $t$ hours. We can set up equations for the heights of the candles as they burn. $\newline$ First candle's height after $t$ hours: $15 - \frac{5}{6}t$ $\newline$ Second candle's height after $t$ hours: $25 - 2.5t$
Solve for Time: We want to find the time $t$ when both candles are the same height, so we set the equations equal to each other: $\newline$ $15 - \frac{5}{6}t = 25 - 2.5t$
Calculate Height When Candles are Same: To solve for $t$ , we'll first get rid of the fractions by multiplying everything by $6$ : $6(15) - 5t = 6(25) - 15t$
Calculate Height When Candles are Same: To solve for $t$ , we'll first get rid of the fractions by multiplying everything by $6$ : $6(15) - 5t = 6(25) - 15t$ Now we simplify: $90 - 5t = 150 - 15t$
Calculate Height When Candles are Same: To solve for $t$ , we'll first get rid of the fractions by multiplying everything by $6$ : $6(15) - 5t = 6(25) - 15t$ Now we simplify: $90 - 5t = 150 - 15t$ Add $15t$ to both sides and subtract $90$ from both sides: $10t = 60$
Calculate Height When Candles are Same: To solve for $t$ , we'll first get rid of the fractions by multiplying everything by $6$ : $6(15) - 5t = 6(25) - 15t$ Now we simplify: $90 - 5t = 150 - 15t$ Add $15t$ to both sides and subtract $90$ from both sides: $10t = 60$ Divide both sides by $10$ to solve for $t$ : $t = \frac{60}{10}$ $t = 6$ hours
Calculate Height When Candles are Same: To solve for $t$ , we'll first get rid of the fractions by multiplying everything by $6$ : $6(15) - 5t = 6(25) - 15t$ Now we simplify: $90 - 5t = 150 - 15t$ Add $15t$ to both sides and subtract $90$ from both sides: $10t = 60$ Divide both sides by $10$ to solve for $t$ : $t = \frac{60}{10}$ $t = 6$ hoursNow we'll plug $t$ back into one of the original height equations to find the height of the candles when they're the same. Let's use the first candle's equation: $\text{Height} = 15 - (\frac{5}{6})(6)$
Calculate Height When Candles are Same: To solve for $t$ , we'll first get rid of the fractions by multiplying everything by $6$ :
$6(15) - 5t = 6(25) - 15t$ Now we simplify:
$90 - 5t = 150 - 15t$ Add $15t$ to both sides and subtract $90$ from both sides:
$10t = 60$ Divide both sides by $10$ to solve for $t$ :
$t = \frac{60}{10}$
$6$ $0$ hours Now we'll plug $t$ back into one of the original height equations to find the height of the candles when they're the same. Let's use the first candle's equation:
Height = $6$ $2$ Simplify the calculation:
Height = $6$ $3$
Height = $10$ cm