I assume you are familiar with integration or differential equations.
y(t)=amount of air (in c.f.) in room at time t.
=rate of increase of fresh air per unit time (min)
=fresh air in - fresh air out per minute
=600 - 600(y/20000)
Separate variables and integrate:
∫dy/(20000-y) = (600/20000)∫ dt
-log(20000-y) = 600t/20000 + C'
log(20000-y) = -600t/20000 + C
Raise to power of e:
20000-y = e^(-600t/20000+C)
At t=0, y=0
=77 minutes (approx.)
thanks for your help
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