AlgebraVery hardTime from a drain-then-fill sequence
Algebra practice question
A tank is drained at 3 litres per minute for m minutes and then filled at 5 litres per minute for m + 4 minutes. At the end it holds 32 litres more than it did at the start. What is the value of m?
Answer: 6
Change in volume: −3m + 5(m + 4) = 32, so 2m + 20 = 32 and m = 6.
Common wrong answers
- If you answered 16
- 16 comes from 2m = 32, forgetting the 20 litres from the extra 4 minutes of filling.
- If you answered 26
- 26 comes from 2m − 20 = 32, subtracting the 20 instead of adding it.
- If you answered 1.5
- 1.5 comes from 8m + 20 = 32, adding the rates instead of subtracting the drain.
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