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In my house, we drink the groundwater that we get from our well. It is 40 meters deep. The question is, how old is the water that we drink today? Is it from the rain 100 years ago?

Another issue is, today much pesticide is used. Someday they will diffuse down to the underground 40 meter. How long will it take?

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    $\begingroup$ That's two different questions in one post. We would like to have one question per post. Can you please split out the pesticide question and post it as a new question? $\endgroup$ – gerrit May 8 '17 at 11:15
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    $\begingroup$ If this were Physics or Astronomy SE, it would be necessary to point out that most water molecules are billions of years old. $\endgroup$ – Spencer May 8 '17 at 23:54
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    $\begingroup$ Not a direct answer to your question but one of the most likely ways for pesticide contamination to get into your well water is downward along the outside of the bore casing. Many water supply wells, particularly older ones are not sealed very well. You could consider adding surface seal of bentonite clay or cement. And be sure not to wash out pesticide containers or tanks near the well! $\endgroup$ – haresfur May 10 '17 at 3:30
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The age of groundwater can vary over a large span. The moment a drop of rain enters the ground it becomes groundwater and when it reaches the groundwater table, the water starts to flow towards a lower hydrostatic level, usually towards the sea, a river or a lake. If you have a well, you'll pump up water to lower the hydrostatic level near the well, so that local groundwater will flow towards the well instead of the ocean.

The velocity of the flow depends on a number of parameters. Naturally, the distance from the recharge area, the hydrostatic pressure, that is the elevation difference over the flow, and finally but not least important, the permeability of the soil and rocks it flows through. If the ground consists of e.g. porous sand, gravel from outwash planes or very fractured rocks the water will flow fast towards a lower level, but if the ground in impermeable, eg. shale or igneous rocks without cracks, the flow will be much slower.

Creative Commons Attribution-Share Alike 3.0 Unported USGS

If you have sandy ground, and shallow groundwater table, the pesticides will reach the groundwater table in very short time (maybe days?), if the aquifer is covered by clay, it might take millennia. It also depends on the unsaturated zone and the mosture above the groundwater table.

So, unfortunately, it's impossible to answer your question(s) without more information. Shallow groundwater is typically from zero to a couple of hundred years old. Some thousand years are not uncommon and for deep aquifer (that have little hydrostatic pressure reason to flow towards an ocean). It can be millions or even billion years old.

The age of groundwater can be detected by Carbon-14 decay or by measuring known contamination, eg. CFCs, depending on the age range.

If you are worried about contamination of you your well, apart from analyse the water, I'd make some sketches of the groundwater flow, e.g. map nearby rivers (river surface = groundwater surface) and the hydrostatic level (well water surface) in your well to find out what direction the water and contamination flow. If the contamination is between you and a river, the best guess would be that the contamination flows away from you, but if you pump up alot of water, the gradient of the groundwater table might change and the contaminations flow toward your well instead of the river.

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Groundwater ages vary enormously across the globe and with depth: from hours in parts of Florida and areas with Karstic geology, to tens of thousands of years in the American breadbasket, all the way to several billion years as was recently discovered in Canada. Remember that some of this groudwater may be perfectly drinkable, while by far, most of it will be a hot, salty, crappy-tasting mess.

As for how long will it take for pesticide to travel down 40 meters.... that all depends on the hydraulic conductivity of everything between the source and your groundwater: a thin clay layer may be enough to block all downward progress and divert flow horizontally, extending the travel-time considerably. In dry areas of the Western US, for example, a pesticide spill will NEVER successfully travel vertically downward to the water table as there is not enough rain to force percolation to depth.

Also, remember that pesticide toxicity is time dependent, especially in the sub-surface. A given pesticide will react with water chemistry, soil minerals, and with groundwater bacteria; it begins decomposing immediately and doesn't stay poisonous forever. Hydrogeologist can effectively date the source of a pesticide (and most common contaminants) plume by looking at degradation products.

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