Aswimming pool whose volume is 10,000 gal contains water that is 0.01% chlorine. starting at t = 0, city water containing0.001% chlorine is pumped into the pool at a rate of 5 gal/min. the pool water flows out at the same rate. what is thepercentage of chlorine in the pool after 1 h? when will the pool water be 0.002% chlorine?

a) The percentage of chlorine after 1 hour is 0.00973%.

b) The pool water will habe a concentration of 0.002% chlorine at 4394 minutes (or 73.24 hours).

Step-by-step explanation:

We can define as X(t) the amount of chlorine that is in the pool at time t.

Then, the rate of change of X can be written as

being Ci the concentration of chlorine of the inflow (0.001%), f_in the inflow (5 gal/min) and f_out the outflow (the same as the inflow, 5 gal/min).

When t=0, the concentration is 0.01%, so the amount of chlorine X is

Replacing in the equation, we have

The amount of chlorine for any time t is then

a) At one hour (t=60 min), the amount of chlorine is

This amount means a concentration of

b) A concentration of 0.002% of chlorine means an amount of chlorine of

Then we can calculate