Answer:
B. They will never have the same amount of water because the solution to the system is (-2,18). It is not possible to have time be -2 hours.
Step-by-step explanation:
Let us assume that
x = the number of hours the tanks are filling,
y = the number of gallons in the tank.
Tank 1 contains 12 gal of water and is leaking at a constant rate of 3 gal/h.
As the water is decreasing with time, so rate of change will be negative, so the equation will be
[tex]y=12-3x[/tex] --------------1
Tank 2 contains 8 gal of water and is leaking at a constant rate of 5 gal/h.
As the water is decreasing with time, so rate of change will be negative, so the equation will be
[tex]y=8-5x[/tex] --------------2
As we have to calculate the time where the amount of water left in the tanks will be same, so
[tex]\Rightarrow 12-3x=8-5x[/tex]
[tex]\Rightarrow 5x-3x=8-12[/tex]
[tex]\Rightarrow 2x=-4[/tex]
[tex]\Rightarrow x=-2[/tex]
So, at x= -2, y will be
[tex]y=12-3(-2)=12+6=18[/tex]
Here, x which is time, is negative i.e solution is not possible.
Also the value of y comes out to be 18, which is impossible. Because there is not even 18 gal of water, so how can they both have 18 gal water.
