Your municipality withdraws 10,000 gallons per day from an aquifer that originally held 1,000,000 gallons. The recharge rate to the aquifer is 2,000 gallons per day. How long will it take before the aquifer is depleted?
You have to make an equation that relates the amount of water (w) in the aquafier to time (t).
Start with the original amount:
$\displaystyle w(t) = 1000000$
Now, we know that every day ten thousand gallons are taken out so we have:
$\displaystyle w(t) = 1000000 - 10000t$
And we also know that every day two thousand gallons are added so we have:
$\displaystyle w(t) = 1000000 - 10000t + 2000t$
$\displaystyle w(t) = 1000000 - 8000t$
To find when the water runs out, set the equation equal to 0 and solve for t:
$\displaystyle 1000000 - 8000t = 0$
$\displaystyle
8000t = 1000000$
$\displaystyle t = 125$
So, the water will run out after 125 days.