On Monday, a dental hygienist cleans teeth of 5 patients by the time she takes her lunch break at noon. On average, she is able to clean the teeth of 9 patients in 4 hours.

Question

Write a function to represent the number of patients she sees, , and the number of hours, , the hygienist works after lunch on Monday.

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Answer 1

To determine the relationship between the number of patients cleaned (denote as \( p \)) and the number of hours worked (denote as \( h \)), we start by establishing the rate of cleaning based on the information given.

From the problem statement, we know:

1. The hygienist cleans the teeth of 5 patients by noon, and she takes a lunch break at that time.
2. The average rate is 9 patients in 4 hours.

First, we can find the rate of cleaning:

\[ \text{Rate} = \frac{\text{Patients}}{\text{Hours}} = \frac{9 \text{ patients}}{4 \text{ hours}} = 2.25 \text{ patients per hour} \]

Now, if \( h \) represents the number of hours worked after lunch, the number of patients she sees after lunch can be given by:

\[ p = 2.25h \]

This equation captures the number of patients \( p \) in terms of the hours \( h \) that the hygienist works after lunch.