Advanced MathMediumTime from a quadratic volume model
Advanced Math practice question
Water flows into a tank so that the volume of water in it, in litres, t minutes after the flow starts is V(t) = t² + 6t. After how many minutes is the volume 40 litres?
Answer: 4
t² + 6t = 40 → t² + 6t − 40 = 0 → (t + 10)(t − 4) = 0 → t = 4 (time must be positive).
Common wrong answers
- If you answered 40
- 40 is the volume, not the time.
- If you answered -10
- −10 is the rejected negative root.
- If you answered 6.67
- 6.67 comes from 6t = 40, ignoring the t² term.
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