Question

2. 8.F.1.2 A farmer has iwo water tanks that drain at a rate of 2.5 gallons per minute. He is considering replacing the existing tanks with new ones, either Model S or Model T. Information about the new tanks is shown below. Each tank holds 100 galions of water and drains at a constant rate. How do the drainage rates of Model S and Model T compare with the existing tanks? Modal T Drainage Rate 500 Model S Drainage Rate Time (minutes) Quantity Igalors) 4 85 190 Quantity (gallons) 6. Time (minutes)

Answer 1

You know that the two water tanks the farmer has, drain at a rate of 2.5 gallons per minute.

You also know that Model S and ModelT hold 100 gallons of water each.

• Knowing the values given in the table for the tank Model S, you can find the its drainage rate as following:

Use the following formula:

`r_S=(y_2-y_1)/(x_(2-)x_1)`

Using the information given in the table, you can set up that:

`\begin{gathered} y_2=100 \\ y_1=82 \\ _{} \\ x_2=0 \\ _{}x_1=6 \end{gathered}`

Substituting values into the formula and evaluating, you get:

`r_S=(100-82)/(0-6)=(18)/(-6)=(6)/(-2)=-3`

• Analyzing the graph given of Model T drainage rate, you can use the same formula:

`r_T=(y_2-y_1)/(x_(2-)x_1)`

In this case you know these points on the line:

`(0,100);\mleft(4,86\mright)`

Then you can set up that:

`\begin{gathered} y_2=100 \\ y_1=86 \\ x_2=0 \\ x_1=4 \end{gathered}`

Substituting values and evaluating, you get:

`r_T=(100-86)/(0-4)=(14)/(-4)=(7)/(-2)=-3.5_{}_{}`

Therefore, notice that:

- Model S Drainage rate is:

`3\text{ }(gallons)/(minute)`

- Model T Drainage rate is:

`3.5\text{ }(gallons)/(minute)`

The answer is: Model S and Model T drain faster than the existing tanks.