Stephen H. answered 02/23/22
Tutor of Math, Physics and Engineering ... available online
300-40t ... 0<t<3
180 -20(t-3) ... 3<t<12
Elizabeth Elaine R.
asked 02/23/22A 500-gallon backyard swimming pool that contains 300 gallons of water is being drained through a hose. During the first 3 hours, the pool drains at a rate of 40 gallons per hour. During the next 9 hours the pool drains at a rate of 20 gallons per hour. Which of the following functions represents the volume of water in the pool at time t, where 0 <= t <= 12 ?
Stephen H. answered 02/23/22
Tutor of Math, Physics and Engineering ... available online
300-40t ... 0<t<3
180 -20(t-3) ... 3<t<12
This is algebra, not Differential equations: The rates are constant and subtract from the volume proportional to the time.
From 0 to 3 hours: V = 300 - 40t
After 3 hours, the new volume is 300 - 120 = 180 and if you want to use the original t, you need for the function to start emptying at t = 3 seconds:
from 3 to 9 hours V = 180 - 20(t-3)
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