Two candles are lit at the same time. Candle A is 24... | SAT Linear equations in one variable Question, Answer Explained

Question bank / Linear equations in one variable

Math · AlgebraMedium

Two candles are lit at the same time. Candle A is $24$ centimeters tall and burns $1.5$ centimeters per hour. Candle B is $18$ centimeters tall and burns $0.75$ centimeter per hour. After how many hours will the two candles be the same height?

$4$

$8$

$12$

$16$

Show answer and explanation

Answer: B

After $t$ hours, candle A is $24 - 1.5t$ centimeters tall and candle B is $18 - 0.75t$ centimeters tall. Set these equal: $24 - 1.5t = 18 - 0.75t$ . Then $6 = 0.75t$ , so $t = 8$ .

Choice C, $12$ , is the height of each candle after $8$ hours, not the number of hours.

Why the other choices are wrong

A. This divides the 6 centimeter difference by 1.5. The gap closes by only 1.5 - 0.75 = 0.75 centimeter per hour.
C. 12 centimeters is the height of both candles after 8 hours, not the number of hours.
D. 16 hours is when candle A burns down completely, 24 divided by 1.5.

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