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AlgebraHardWhen two linear models meet

Algebra practice question

Candle A is 20 centimetres tall and burns down at 2 centimetres per hour. Candle B is 14 centimetres tall and burns down at 0.5 centimetres per hour. Both are lit at the same time. After how many hours will the two candles be the same height?

Answer: 4

Heights after t hours: A is 20 − 2t and B is 14 − 0.5t. Set them equal: 20 − 2t = 14 − 0.5t, so 6 = 1.5t and t = 4. Check: both are 12 centimetres tall at t = 4.

Common wrong answers

If you answered 6
6 is the difference in starting heights (20 − 14). Divide it by the difference in burn rates (2 − 0.5 = 1.5) to get the time: 4 hours.
If you answered 10
10 is when candle A burns out (20 / 2). By then candle B is 9 centimetres tall — they were equal earlier, at 4 hours.
If you answered 2.4
2.4 is 6 / 2.5, ADDING the rates. Both candles shrink, so the gap closes at the DIFFERENCE of the rates, 1.5 cm per hour.

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