Fermi Estimate: Filling a 50-Meter Competition Pool With One Garden Hose

Estimate how long it would take to fill an Olympic-size swimming pool using one garden hose. ```hint Two numbers decide it The answer is the pool's volume divided by the hose's flow rate. Anchor the flow rate in something you have seen, such as how long a bucket takes to fill. ``` ### Clarifying Questions - May I use the standard 50 m by 25 m competition footprint, and which depth should I assume, since competition pools vary? - Is this one ordinary household hose at normal tap pressure, running nonstop until the pool is full? - Should I ignore losses such as evaporation and leaks? - Do you want a single number or a range, and in what time unit? ### What a Strong Answer Covers - A clear structure: fill time equals pool volume divided by hose flow rate - A justified pool volume with stated dimensions and correct unit conversions - A flow rate anchored in an everyday reference rather than pulled from thin air - Arithmetic carried through to a human-scale answer, with a sanity check - Sensitivity: which assumptions (depth, hose size, water pressure, evaporation) move the result most ### Follow-up Questions - How many hoses would you need to fill the pool over a single weekend, and what would stop that from working in practice? - How would you estimate what the water for the fill would cost? - Which assumption would you firm up first, and how would you do it in five minutes?