Question

Milly reads 20pages in 4 minutes. Sara reads 12pages 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 both Milly and Sara, we need to determine how many pages they read per minute.

**For Milly:**
- Milly reads 20 pages in 4 minutes.
- We can find her reading rate (pages per minute) by dividing the number of pages by the number of minutes:
\[
\text{Reading rate for Milly} = \frac{20 \text{ pages}}{4 \text{ minutes}} = 5 \text{ pages per minute}
\]

The equation that represents the direct variation for Milly can be written as:
\[
y = 5x
\]
Where \( y \) is the number of pages read and \( x \) is the number of minutes.

**For Sara:**
- Sara reads 12 pages in 3 minutes.
- We can find her reading rate by dividing the number of pages by the number of minutes:
\[
\text{Reading rate for Sara} = \frac{12 \text{ pages}}{3 \text{ minutes}} = 4 \text{ pages per minute}
\]

The equation that represents the direct variation for Sara can be written as:
\[
y = 4x
\]
Where \( y \) is the number of pages read and \( x \) is the number of minutes.

In summary:
- Milly's direct variation equation is \( y = 5x \) with a constant of proportionality of 5 pages per minute.
- Sara's direct variation equation is \( y = 4x \) with a constant of proportionality of 4 pages per minute.