Question

4. a new office Residential-Building just opened in Lagrangeville and a contractor is monitoring the water use. for the most part, water is used by the office between the hours of 7AM - 7PM and in the residential section between 12AM - 9PM or 3PM - 12AM, including the endpoint times. (a) create a compound inequality written in an interval notation that represents the hours that both sections (residential an office) are using water at the same time. graph the solution on the number line given. assume that 12AM correspond to zero and a time such as 3PM corresponds to 15. as a start, it might help to graph each individual section's water use and see where they overlap. (b) if the water heater in the building cannot sustain more than 4 hours of use from both parties at the same time, will there be a period of the day that cold water will start to be produced? explain

Answer 1

Let 0 represents 12AM

Let 12 represents 12PM

Let 15 represents 3PM in that format

Office residents uses water between 7AM to 7PM

That represents from 7 to 19

Case 1

If Resisdential section uses Water from 12AM to 9PM

That represents 0 to 21

In this case, both of sections will use water from 7 to 19 at the same time.

Representing In inequality form, we have

`\begin{gathered} 7\text{ }\leq\text{ t }\leq\text{ 19} \\ \text{where t represents the time of the day} \end{gathered}`

The graph of the Solution is

Case 2

f Resisdential section uses Water from 3PM to 12AM

That represents 15 to 24 (note that 24 also means 0)

In this case, both of sections will use water from 15 to 19 at the same time.

Representing In inequality form, we have

`15\leq t\leq19`

The graph of the solution is

Part b

Yes , there will be a period when cold water will start to produced . The period is in case 1 above because both sections will be using water for more than 4 hours at thesame time