Question

Two tanks are being drained of water . The table shows the volume of water in Tank X over time. The graph shows the volume of water in Tank Y over time. Part A which tank is draining at the faster rate ? A. Tank X. B. Tank Y Part B what is the difference in the rates the tanks are draining? Enter the answer in box.

Answer 1

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:

`m=(y_2-y_1)/(x_2-x_1)`

Taking a pair of points from the table:

`\begin{gathered} (x_1,y_1)=(0,14) \\ (x_2,y_2)=(1,12) \end{gathered}`

Replacing in the formula:

`m_X=(12-14)/(1-0)`

Solving the operations:

`m_X=-2`

For tank Y:

`\begin{gathered} (x_1,y_1)=(1,14.5) \\ (x_2,y_2)=(4,10) \end{gathered}`

Replacing in the formula:

`m_Y=(10-14.5)/(4-1)`

Solving the operations:

`m_Y=-(4.5)/(3)=-1.5`

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:

`2-1.5=0.5`

The difference is 0.5 gallons/min.