Mai is filling her fish tank water flows into the tank at a constant rate. 2.&- 0.5 1.6 time (minutes) water (gallons) 0.5 0.8 1 x1.6 1.6 x1.6 4.8 25 G 3 40 1) How many gallons of water will be in the fish tank after 3 minutes? Explain or show your reasoning. 2) How long will it take to fill the tank with 40 gallons of water? Explain or show your reasoning. 3) What is the constant of proportionality? What does it tell us about this situation?



Answer :

Given

x = 0.5; y = 0.8

The constant of proportionality has to be calculated to estimate the other values.

The constant of proportionality "k" determines the relation of x and y, which can be represented as: y = kx.

So, in this exercise,

[tex]\begin{gathered} 0.8=k\cdot0.5 \\ \frac{0.8}{0.5}=k \\ k=1.6 \end{gathered}[/tex]

y = 1.6y

(1) From this, we can estimate the value of y when x = 3.

[tex]\begin{gathered} y=1.6\cdot3 \\ y=4.8\text{gallons} \end{gathered}[/tex]

(2) If we want how long it will take to fill the tank with 40 gallons:

[tex]\begin{gathered} 40=1.6\cdot x \\ \frac{40}{1.6}=x \\ 25=x \end{gathered}[/tex]

It will take 25 minutes.

(3) Finally, the constant of proportionality is 1.6 (as calculated above).

It tells us that the ratio between the gallons water of water and time. In other words, it tells us that for each 1 minute, 1.6 gallons are filled.