Question

I need to know the answer but I need to know how to get it and work it out

Answer 1

Let's start by completing the first table.

The questions gives the depth in two times:

- 2 hours after start -> 64 inches of water

- 4 hours after start -> 48 inches of water

From this, we can identifythe units:

- for time, we will use hours

- for depth, we will use inches

The first given values are:

- for time, 2

- for depth, 64

The second given valuesa are:

- for time, 4

- for depth, 48

So, the table is:

Quantity Name | Time | Depth of Pool

Unit | hour | inch

Given Value 1 | 2 | 64

Given Value 2 | 4 | 48

Now, we need to calculate the slope, which can be done using the given points and the equation:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(48-64)/(4-2) \\ m=(-16)/(2) \\ m=-8 \end{gathered}`

So, the slope is -8 inches per hour.

The interceptwe the b in the equation:

`y=mx+b`

Where y is the depth and x is the time. So, using the first given values and the slope, we can find b:

`\begin{gathered} 64=-8\cdot2+b \\ 64=-16+b \\ b=64+16 \\ b=80 \end{gathered}`

Thus, the intercept is 80 inches.

So, the formula we have for the pump is:

`y=-8x+80`

Using it, we can answer questions 1 and 2:

1. After 6 hours means x = 6, so:

`\begin{gathered} y=-8\cdot6+80 \\ y=-48+80 \\ y=32 \end{gathered}`

So, y = 32, thus, the depth of the water will be 32 inches.

2. The level 24 inches mean y = 24, so:

`\begin{gathered} 24=-8x+80 \\ 8x=80-24 \\ 8x=56 \\ x=(56)/(8) \\ x=7 \end{gathered}`

Thus, x = 7, and the water will be at 24 inches after 7 hours.