Estimation question
How long would it take to empty a hot tub using only a drinking straw?
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What this question tests
Quick physical estimation using flow rate reasoning, checking whether you can build a simple model instead of guessing a number.
How to approach it
- Clarify assumptions: a standard hot tub holds roughly 1,500 liters, and a drinking straw has an inner diameter of about 5 millimeters.
- Model the straw as a siphon or suction tube, since gravity draw or manual suction determines flow rate, and assume manual suction at a comfortable sustained rate.
- Estimate flow rate through the straw: a person can realistically draw and expel roughly 20 to 30 milliliters per suction cycle, at about 1 cycle per second, so 20 to 30 mL per second if sustained, though real sustained rates are far lower due to fatigue.
- Adjust for a more realistic sustained rate, since no person could suction constantly for hours, so assume a mechanical or automated siphon drawing at a steady 10 mL per second instead.
- Compute time: 1,500 liters divided by 10 mL per second equals 150,000 seconds, roughly 41.7 hours.
- State the answer as an order of magnitude, roughly 1.5 to 2 days of continuous flow, and flag that human suction alone is impractical, so a passive siphon assumption is more realistic.
What a strong answer includes
- Recognizes that manual human suction is not sustainable and reframes the problem as a passive siphon, a key insight many candidates miss.
- States the tub volume and straw flow rate as explicit assumptions, making the chain of logic easy to follow and challenge.
- Lands on an order-of-magnitude answer, around 1.5 to 2 days, framed appropriately as an estimate, not a precise figure.
Common mistakes
- Assuming a person could physically suction continuously for the full duration, ignoring fatigue and giving an unrealistic flow rate.
- Skipping unit conversion between liters and milliliters, leading to an answer off by several orders of magnitude.
Likely follow-up questions
- How would the answer change with a wider straw, like a smoothie straw?
- What's the biggest source of error in this estimate?
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Learn the skill behind it
Chapters of the AI PM course that teach what this question tests.
- Chapter 2: Data fluency: SQL, logs, and reading the truth yourself
- Chapter 9: Prove it paid off: outcomes, economics, and pricing
- Chapter 14: Get the job: the AI PM interview loop