We are given that two tanks are draining in a linear form. To determine the rate of draining we need to determine the slope of the lines for each tank. The slope is given by the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Taking a pair of points from the table:
[tex]\begin{gathered} (x_1,y_1)=(0,14) \\ (x_2,y_2)=(1,12) \end{gathered}[/tex]
Replacing in the formula:
[tex]m_X=\frac{12-14}{1-0}[/tex]
Solving the operations:
[tex]m_X=-2[/tex]
For tank Y:
[tex]\begin{gathered} (x_1,y_1)=(1,14.5) \\ (x_2,y_2)=(4,10) \end{gathered}[/tex]
Replacing in the formula:
[tex]m_Y=\frac{10-14.5}{4-1}[/tex]
Solving the operations:
[tex]m_Y=-\frac{4.5}{3}=-1.5[/tex]
Therefore, the rate of change of tank X is 2 gallons/min and tankY 1.5 gallons/min. Tank X has a greater rate of drain.
The difference is:
[tex]2-1.5=0.5[/tex]
The difference is 0.5 gallons/min.
