Question

Milly reads 20pages in 4 minutes. Sara reads 12 pages in 3 minutes. Find each constant of proportionality and write a direct variation equation for each

Answer 1

To find the constant of proportionality for each person, we can determine their reading rates in pages per minute. Then we can write a direct variation equation for each.

### For Milly:
Milly reads 20 pages in 4 minutes.

First, calculate her reading rate:

\[
\text{Rate} = \frac{\text{Number of pages}}{\text{Time in minutes}} = \frac{20 \text{ pages}}{4 \text{ minutes}} = 5 \text{ pages/minute}
\]

The constant of proportionality (k) for Milly is 5. The direct variation equation can be written as:

\[
p = 5t
\]

where \( p \) is the number of pages read and \( t \) is the time in minutes.

### For Sara:
Sara reads 12 pages in 3 minutes.

Now calculate her reading rate:

\[
\text{Rate} = \frac{\text{Number of pages}}{\text{Time in minutes}} = \frac{12 \text{ pages}}{3 \text{ minutes}} = 4 \text{ pages/minute}
\]

The constant of proportionality (k) for Sara is 4. The direct variation equation can be expressed as:

\[
p = 4t
\]

where \( p \) is the number of pages read and \( t \) is the time in minutes.

### Summary:
- **Milly:** Constant of proportionality = 5
- Direct variation equation: \( p = 5t \)

- **Sara:** Constant of proportionality = 4
- Direct variation equation: \( p = 4t \)