# Question: your swimming pool containing 70000 gal of water has been...

###### Question details

Your swimming pool containing 70,000 gal of water has been contaminated by 7 kg of a nontoxic dye that leaves a swimmer's skin an unattractive green. The pool's filtering system can take water from the pool, remove the dye, and return the water to the pool at a flow rate of 250 gal/min. Assume that the dye is uniformly distributed throughout the pool.

**(a)** What is the initial value problem for the
filtering process; let *q*(*t*) be the amount of dye
in the pool at any time *t*. What is the initial amount of
the dye in the pool?

Enter the exact, fully simplified answer. Use *q* as
*q*(*t*).

dq/dt = ____ g/min

q(0) = _____ grams

**(b)** Solve for *q*(*t*) from part
**(a)**.

Do not use thousands separator in the answer field.

q(t) = _____ grams

**(d)** Find the time *T* at which the
concentration of the dye first reaches the value of 0.02 g/gal.

Round your answer to two decimal places.

T = _____ hours

**(e)** Find the flow rate *r* that is
sufficient to achieve the concentration 0.02 g/gal within 4 h.

Round your answer to the nearest integer.

r = _____ gallons/minute