SAC-Style Question \( 4: \mathrm{H} \omega \) Two candles are burning. Candle \( A \) is initially 12 cm and candle \( B 16 \mathrm{~cm} \). If candle \( A \) burns at \( 0.8 \mathrm{~cm} / \mathrm{hr} \) and candle B at \( 1.5 \mathrm{~cm} / \mathrm{hr} \), how long does it take for both candles to be the same height?
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To determine when both candles will be of equal height, we can use their initial heights and burn rates to create an equation. Candle A's height after \( t \) hours is given by: \( H_A = 12 - 0.8t \) Candle B's height after \( t \) hours is given by: \( H_B = 16 - 1.5t \) We set these two equations equal to each other to find the time \( t \) when both heights are the same: \( 12 - 0.8t = 16 - 1.5t \) Rearranging gives: \( 1.5t - 0.8t = 16 - 12 \) \( 0.7t = 4 \) \( t = \frac{4}{0.7} \approx 5.71 \) hours. Thus, it will take approximately \( 5.71 \) hours for both candles to reach the same height. But here's the fun fact: candle burning rates do not just depend on their heights but also on the wax composition! Different materials can burn faster or slower, creating unique effects in time. Have you ever tried timing your candle burn alongside a good book? It can turn the mundane into a delightful experience, marking a moment where activity and relaxation vibe perfectly together! Lighting a scented candle while getting lost in a novel not only sets the mood but also makes every flicker of the flame tell a story of its own.
