# Math Help - How to work out percentage from formula

1. ## How to work out percentage from formula

Hi

I have a question which states that there is water tank with 1 000 000 litres of water and has been tainted with arsenic the % of aresenic is 0.12%
To make it safe it needs to diluted to a level of 0.001% the tank hold 45 000 000 litres of water

Water can be pumped in at 40 000litres per hour

From that i worked out a formula to work out the percentage but cant go from a percentage back to number of hours that fresh water needs to pumped in

T=hr of water pumped

T=120 000/(40 000*T+880 000)

where 120 000 is the amount of arsenic in the water
880 000 is the amount of water mixed with the arsenic
40 000 is how much water er hour can be pump in to dilute the solution

Need to get a % of 0.001 can someone show me how from this information how long the pump will have to be on

Cheers Trappl

2. ## Re: How to work out percentage from formula

Hello, Trappl!

Also, is there some information missing?
As stated, the problem has no solution.

There is water tank with 1,000,000 litres of water and has been tainted with arsenic.
The % of arsenic is 0.12%. .This is 0.0012
To make it safe, it needs to diluted to a level of 0.001%. .This is 0.00001
The tank hold 45 000 000 litres of water
Water can be pumped in at 40,000 litres per hour.

Presently the tank has $0.0012\times1,\!000,\!000 \,=\,1200$ liters of arsenic.

We will add $x$ liters of water.

Then: . $\frac{1200}{x+1,\!000,\!000} \:=\:0.00001 \quad\Rightarrow\quad 1200 \:=\:0.00001x + 10$

. . . . . $0.00001x \:=\:1190 \quad\Rightarrow\quad x \:=\:\frac{1190}{0.00001} \:=\:119,\!000,\!000$

Hence, we must add 119 million liters of water.
But the tank hold only 45 million liters.
We're stuck . . .