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: \( p = 5t \)
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Sara: Constant of proportionality = 4
- Direct variation equation: \( p = 4t \)
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