The table below shows the number of math questions completed by Olivia with respect to time.

Math Questions 12 16 20 24 28
Time (minutes) 36 48 60 72 84

Which of the following statements gives the unit rate?
A.
For every question, Olivia takes 4 minutes.
B.
In every minute, Olivia solves 2.5 questions.
C.
In every minute, Olivia solves 2 questions.
D.
For every question, Olivia takes 3 minutes.

1 answer

To find the unit rate, we need to calculate how many math questions Olivia completes in one minute.

Looking at the data provided:

When Olivia completes 12 questions, it takes her 36 minutes.
When she completes 16 questions, it takes her 48 minutes.
When she completes 20 questions, it takes her 60 minutes.
When she completes 24 questions, it takes her 72 minutes.
When she completes 28 questions, it takes her 84 minutes.

To find the average rate, we can use the total questions completed over the total time:

Calculate the total number of questions and the total time used. We can take any of the sets. For example, using the 28 questions:

Time = 84 minutes
Questions = 28

Now, we find the number of questions per minute:

\[ \text{Unit rate} = \frac{\text{Number of Questions}}{\text{Time in Minutes}} = \frac{28}{84} = \frac{1}{3} \quad (\text{questions per minute}) \]

This means Olivia solves \(\frac{1}{3}\) of a question per minute or, equivalently, it takes her 3 minutes to solve one question.

This corresponds to option D:

D. For every question, Olivia takes 3 minutes.

Therefore, the correct answer is D.