The completed table for the amount of water in the tank at the given time given a constant flow rate of 1.6 is given below :
- Time(t) __ Water(W)
- 0.5 _______ 0.8
- 1 _________ 1.6
- 3 _________4.8
- 25 ________ 40
From the table given :
0.8 gallons of water flowed into the tank in 0.5 minutes ;
Since the flow rate is constant ; we can relate the amount of water, w, flowing into the tank at time, t as thus ;
w α t
w = kt ; where, k = constant of proportionality ;
We can obtain the value of k when w = 0.8 and t = 0.5
Therefore,
0.8 = 0.5k
Divide both sides by 0.5
(0.8÷0.5) = k
k = 1.6
Hence the flow rate of water into the tank is 1.6 ; the equation can be then be written thus ;
w = 1.6t
Let's find ;
w, when t = 1
w = 1.6(1)
w = 1.6
w, when t = 3
w = 1.6(3)
w = 4.8
4.8t, when w = 40
40 = 1.6t
Divide both sides by 1.6
(40 ÷ 1.6) = t
t = 25
Therefore, the constant of proportionality, k is 1.6
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