Question

An electrician is hired to install a ceiling fan. She estimates that the installation will take no more than 45 minutes if the house is up to building code. If the house is not up to building code, she estimates that the installation will take longer than 120 minutes. Which graph represents the number of minutes it could take her to install the fan?

Answer 1

To represent the time it could take the electrician to install the ceiling fan based on whether the house is up to building code or not, we can break it down into two scenarios:

1. If the house is **up to building code**, the installation time is between 0 and 45 minutes inclusive. This can be represented on a number line or graph as a segment from 0 to 45, including both endpoints.

2. If the house is **not up to building code**, the installation time is greater than 120 minutes. This means that the graph should show a segment starting just above 120 and extending indefinitely.

### Graph Representation:

- On the graph:
- The segment from 0 to 45 minutes should be represented with a solid line (or filled dot) at both 0 and 45 to indicate that these values are included.
- There should be a separate part of the graph that starts just above 120 minutes and extends infinitely to the right, which can be indicated by an open dot at 120 and an arrow extending right, showing that all times greater than 120 are included.

In summary, the graph will have:
- A filled line segment between 0 and 45 (inclusive).
- An open circle at 120, with an arrow extending to the right to indicate times greater than 120.

This visual representation would effectively show the possible time ranges for the installation based on whether building code standards are met.