Candles

Algebra Level 3

I have 2 candles. Both are of the same height, and each candle burns at a constant rate. The first candle takes 5 hours to burn completely while the second candle takes 4 hours to burn completely. Find the time in minutes for the height of the first candle to be 4 times the height of the second candle if both are lit at the same time.


The answer is 225.

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Yuxuan Seah by Yuxuan Seah , 20, Singapore

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2 solutions

Nguyen Thanh Long
Aug 20, 2014

Call x is velocity of candle one to burn, y is velocity of candle two. t is the time that We have to find. So We have: h = 5 × x = 4 × y h=5 \times x=4 \times y x = h 5 x=\frac{h}{5} y = h 4 y=\frac{h}{4} h − t × h 5 = 4 ( h − t × h 4 ) = 4 h − t × h h-t \times \frac{h}{5} = 4(h-t \times \frac{h}{4})=4h - t \times h 3 h = 4 t × h 5 3h=4t \times \frac{h}{5} ⇒ t = 60 × 15 4 = 225 \Rightarrow t=60 \times \frac{15}{4} = \boxed{225}

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Solve for t, where 4 times (240 - t)/240 equals (300 - t)/300. Ans:225

Rajen Kapur - 6 years, 9 months ago
Jun Arro Estrella
Dec 19, 2016

L − ( L / 5 ) ( t ) = 4 ( L − ( L / 4 ) ( t ) ) L - (L/5)(t) = 4(L-(L/4)(t))

solve for t and the rest is history

(t is in hours)

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