HOUR MATH WITH MRS. NGUYEN $\newline$ $4$ : Practice \& Problem Solving $\newline$ $5$ . $4$ .PS $-12$ $\newline$ Leonard can read $4$ pages in $15$ minutes. Amy can read $12$ pages in $1$ hour. Explain how you could use a table or graph find how much longer it would take Amy to read a $720$ -page book than Leonard. $\newline$ Make a table of to find how long it takes each to read $\square$ pages. Then, find the It would take Amy $\square$ hours longer to read the book.

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Solve a system of equations using elimination: word problems

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Q. HOUR MATH WITH MRS. NGUYEN

\newline

4

: Practice \& Problem Solving

\newline

5

4

.PS

-12

\newline

Leonard can read

4

pages in

15

minutes. Amy can read

12

pages in

1

hour. Explain how you could use a table or graph find how much longer it would take Amy to read a

720

-page book than Leonard.

\newline

Make a table of to find how long it takes each to read

\square

pages. Then, find the It would take Amy

\square

hours longer to read the book.

Rate Calculation: First, we need to determine the rate at which Leonard and Amy can read pages per minute. $\newline$ Leonard can read $4$ pages in $15$ minutes. To find his rate, we divide the number of pages by the number of minutes. $\newline$ Rate for Leonard = $\frac{4 \text{ pages}}{15 \text{ minutes}} = 0.2667$ pages per minute (rounded to four decimal places).
Leonard's Rate: Next, we calculate Amy's reading rate. Amy can read $12$ pages in $1$ hour ( $60$ minutes). To find her rate, we divide the number of pages by the number of minutes. $\newline$ Rate for Amy = rac{12 ext{ pages}}{60 ext{ minutes}} = 0.2 pages per minute.
Amy's Rate: Now, we will calculate the time it takes for each of them to read a $720$ -page book. $\newline$ For Leonard, we divide the total number of pages by his rate. $\newline$ Time for Leonard = $\frac{720 \text{ pages}}{0.2667 \text{ pages per minute}}$ .
Time Calculation for Leonard: Performing the calculation for Leonard's time: $\newline$ Time for Leonard = $720 / 0.2667 \approx 2700$ minutes.
Leonard's Time Calculation: For Amy, we divide the total number of pages by her rate. $\newline$ Time for Amy = $\frac{720 \text{ pages}}{0.2 \text{ pages per minute}}$ .
Time Calculation for Amy: Performing the calculation for Amy's time: $\newline$ Time for Amy = $720 / 0.2 = 3600$ minutes.
Amy's Time Calculation: To find out how much longer it takes Amy to read the book than Leonard, we subtract Leonard's time from Amy's time. $\newline$ Additional time for Amy = Time for Amy - Time for Leonard.
Additional Time Calculation: Performing the subtraction to find the additional time for Amy: $\newline$ Additional time for Amy = $3600$ minutes - $2700$ minutes = $900$ minutes.
Additional Time in Hours: To convert the additional time from minutes to hours, we divide by $60$ (since there are $60$ minutes in an hour). $\newline$ Additional hours for Amy = $900$ minutes $/$ $60$ minutes per hour.
Additional Time in Hours: To convert the additional time from minutes to hours, we divide by $60$ (since there are $60$ minutes in an hour). $\newline$ Additional hours for Amy = $900$ minutes / $60$ minutes per hour.Performing the division to find the additional hours for Amy: $\newline$ Additional hours for Amy = $900 / 60 = 15$ hours.