AlgebraVery hardTime from a two-stage draining process
Algebra practice question
A tank holds 60 litres. Pump A removes 4 litres per minute. After m minutes, pump B is switched on and adds 1 litre per minute while pump A keeps running. Four minutes after pump B starts, the tank holds 12 litres. What is the value of m?
Answer: 9
In the first m minutes the tank loses 4m litres. In the next 4 minutes the net loss is (4 − 1) × 4 = 12 litres. So 60 − 4m − 12 = 12, giving 4m = 36 and m = 9.
Common wrong answers
- If you answered 7
- 7 comes from a net loss of 5 per minute in the last stage (adding the rates instead of subtracting).
- If you answered 8
- 8 comes from treating the last 4 minutes as a loss of 16 (ignoring pump B): 60 − 4m − 16 = 12.
- If you answered 12
- 12 comes from 60 − 4m = 12, forgetting the last 4 minutes entirely.
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