The amount of water the fish tank of the local pet store can hold is 175 gallons
The tank will be empty after 7.29 hours
From the table given:
- The water in the tank drained at a constant rate.
- Hence, the amount of water in the tank is inversely proportional to time.
We could calculate the drain rate of water per hour ;
Drain rate = change in volume ÷ change in time
Drain rate = (163 - 169) ÷ (1/2 - 1/4) = -6 ÷ 0.25 = - 24 gallons per hour
Amount of water which drains per 0.25 hour = (25 ÷ 4) = 6 gallons
The capacity of the fish tank is the volume of water in the tank at time, t = 0
- At t = 0.25 ; volume = 169
- At t = 0 ; volume = 169 + 6 = 175 gallons
Time when Tank will be empty
Full tank + (drain rate per hour × time) = 0
175 + (-24 × t) = 0
175 - 24t = 0
-24t = - 175
t = 175 ÷ 24
t = 7.29 hours
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