Answer:
a) 9000 L
c) Proof below.
e) 5 hours 23 minutes
Explanation:
Part (a)
The aquarium can be modeled as a rectangular prism.
Note: 1 m³ = 1000 L
Part (b)
Part (c)
4 hours = 4 × 60 minutes = 240 minutes
If it takes 4 hours longer to fill the aquarium with water using tap P as compared to tap Q, then:
Part (d)
Quadratic Formula
Therefore:
Substitute these values into the formula and solve for x:
As the rate is positive only,
Part (e)
If the rate that tap P fills the aquarium with water is x litres per min, and the rate the tap Q fills the aquarium with water is (x+5) litres per min, the rate that both taps fill the aquarium is:
Therefore, if both taps are turned on together, the time it takes to fill the 9000L aquarium is:
Note we really should round up to the nearest minute, even though 23.289... rounded is 23, as if we round down, the aquarium will not quite be filled with water.