# Math Help - Mixture Problem

1. ## Mixture Problem

guys, help me with this, i am still stuck, this is the last one, i am done with all of my work for today.

Consider a reservoir with a volume of 8 billion cubic feet (ft^3) and an initial pollutant concentration of 0.25%. There is a daily of 500 million ft^3 of water with a pollutant concentration of 0.05% and an equal daily outflow of the well mixed water in the reservoir. How long will it take to reduce the pollutant concentration in the reservoir to 0.10%?

2. Originally Posted by DMDil
guys, help me with this, i am still stuck, this is the last one, i am done with all of my work for today.

Consider a reservoir with a volume of 8 billion cubic feet (ft^3) and an initial pollutant concentration of 0.25%. There is a daily of 500 million ft^3 of water with a pollutant concentration of 0.05% and an equal daily outflow of the well mixed water in the reservoir. How long will it take to reduce the pollutant concentration in the reservoir to 0.10%?
The initial volume of pollutant is $p_v(0)=8\time 10^9 \times 0.0025$ cubic ft,

The rate of change of pollutant volume is:

$
p_v'(t)=-(0.5/8)p_v(t)+0.0005 \times 0.5\times 10^9
$
cubic ft per day

and you need to find the time at which $p_v(t)=8\time 10^9 \times 0.001$ cubic ft

CB