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 3 minutes.
B.
In every minute, Olivia solves 2 questions.
C.
In every minute, Olivia solves 2.5 questions.
D.
For every question, Olivia takes 4 minutes.

1 answer

To find the unit rate, we can analyze the data provided in the table.

Olivia completed the following math questions at different times:

  • 12 questions in 36 minutes
  • 16 questions in 48 minutes
  • 20 questions in 60 minutes
  • 24 questions in 72 minutes
  • 28 questions in 84 minutes

Now, let's calculate the rate of questions solved per minute. Here’s the data breakdown:

  1. For 12 questions in 36 minutes: \[ \text{Rate} = \frac{12 \text{ questions}}{36 \text{ minutes}} = \frac{1}{3} \text{ questions per minute} \approx 0.33 \]

  2. For 16 questions in 48 minutes: \[ \text{Rate} = \frac{16 \text{ questions}}{48 \text{ minutes}} = \frac{1}{3} \text{ questions per minute} \approx 0.33 \]

  3. For 20 questions in 60 minutes: \[ \text{Rate} = \frac{20 \text{ questions}}{60 \text{ minutes}} = \frac{1}{3} \text{ questions per minute} \approx 0.33 \]

  4. For 24 questions in 72 minutes: \[ \text{Rate} = \frac{24 \text{ questions}}{72 \text{ minutes}} = \frac{1}{3} \text{ questions per minute} \approx 0.33 \]

  5. For 28 questions in 84 minutes: \[ \text{Rate} = \frac{28 \text{ questions}}{84 \text{ minutes}} = \frac{1}{3} \text{ questions per minute} \approx 0.33 \]

Next, we can find the time taken per question. Inverting the rate gives us:

\[ \text{Time per question} = \frac{36}{12} = 3 \text{ minutes per question} \] \[ \text{Time per question} = \frac{48}{16} = 3 \text{ minutes per question} \] \[ \text{Time per question} = \frac{60}{20} = 3 \text{ minutes per question} \] \[ \text{Time per question} = \frac{72}{24} = 3 \text{ minutes per question} \] \[ \text{Time per question} = \frac{84}{28} = 3 \text{ minutes per question} \]

Thus, Olivia takes 3 minutes for each question, meaning:

Correct Answer: A. For every question, Olivia takes 3 minutes.