Math Is Fun Forum

Ryland

Guest

AP Physics

An average family of 4 uses about 300 gallons of water per day. How much depth would a lake lose per year if it uniformly covered an area of 50 square miles and supplied a local town with a population of 40,000 people? Consider only population uses, and neglect evaporation and so on.

I already have the answer (3 cm). All i need is what i should convert everything to. Basically the work.
Thank you, Ryland.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: AP Physics

Here's what I get:

A population of 40000 people would contain 10000 families, who would therefore use 3 million gallons of water per day between them.

Therefore, ~1095 million gallons are used per year.
Using "a litre of water's a pint and three quarters", this is about 5000 million litres.
One cubic metre contains 1000 litres of water, so the volume drained per year is 5 million cubic metres.

Finally, to get the depth drained, we divide this volume by the area of the lake.

There are about 1600 metres in a mile, which means there are ~2560000 square metres in a square mile, and so the lake has an area of ~128 million square metres.

Therefore, the depth drained is roughly 5/128 = 0.039, or about 4cm.

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It wanted to be normal.