AlgebraHardLast whole minute above a threshold
Algebra practice question
The water level in a tank, in centimetres, t minutes after a drain is opened is 40 − 1.5t. What is the greatest whole number of minutes t for which the level is still above 10 centimetres?
Answer: 19
40 − 1.5t > 10 gives 1.5t < 30, t < 20. The greatest whole number below 20 is 19. (At t = 19 the level is 11.5 cm; at t = 20 it is exactly 10.)
Common wrong answers
- If you answered 20
- At t = 20 the level is exactly 10 cm, not above it.
- If you answered 26
- 26 comes from 40/1.5, when the tank is empty, not when it passes 10 cm.
- If you answered 30
- 30 is 40 − 10, the drop in centimetres, not a time.
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