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Hannah reads at a constant rate of 3 pages every 8 minutes.
Write an equation that shows the relationship between
p, the number of pages she reads, and
m, the number of minutes she spends reading.
Do NOT use a mixed number.

Hannah reads at a constant rate of $3$ pages every $8$ minutes. $\newline$ Write an equation that shows the relationship between $p$ , the number of pages she reads, and $m$ , the number of minutes she spends reading. $\newline$ Do NOT use a mixed number.

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Write linear functions: word problems

Full solution

Q. Hannah reads at a constant rate of

3

pages every

8

minutes.

\newline

Write an equation that shows the relationship between

p

, the number of pages she reads, and

m

, the number of minutes she spends reading.

\newline

Do NOT use a mixed number.

Identify Rate: Identify the constant rate at which Hannah reads. $\newline$ Hannah reads $3$ pages every $8$ minutes. This means that for every $8$ minutes of reading, she completes $3$ pages.
Determine Relationship: Determine the relationship between the number of pages and the number of minutes. $\newline$ Since Hannah reads at a constant rate, the number of pages she reads is directly proportional to the number of minutes she spends reading. We can express this relationship with a proportionality constant, which is the rate of pages per minute.
Calculate Rate: Calculate the rate of pages per minute. $\newline$ To find the rate, we divide the number of pages by the number of minutes. $\newline$ Rate = $\frac{\text{Pages}}{\text{Minutes}}$ = $\frac{3 \text{ pages}}{8 \text{ minutes}}$
Write Equation: Write the equation using the rate. $\newline$ Let $p$ represent the number of pages read and $m$ represent the number of minutes spent reading. The equation that shows the relationship between $p$ and $m$ is: $\newline$ $p = (\text{Rate}) \times m$ $\newline$ $p = \left(\frac{3}{8}\right) \times m$

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