Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Two classmates got together over the weekend to do their assigned History reading. Clarence can read 1 page per minute, while Savannah can read 3 pages per minute. When they met, Clarence had already read 63 pages, and Savannah had already gotten through 33 pages. After a while, they had both read the same number of pages. How many pages had each one read? How long did that take?

Answer 1

Answer:

clearance had read 63 multiply 1 = 63 page read by the Clarence

savannah had already cotton through 33 multiply 3 so she read 99 pages

Step-by-step explanation:

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Two classmates got together over the weekend to do their assigned History reading. Clarence can read 1 page per minute, while Savannah can read 3 pages per minute. When they met, Clarence had already read 63 pages, and Savannah had already gotten through 33 pages. After a while, they had both read the same number of pages. How many pages had each one read? How long did that take

Answer 2

Answer:

Clarence read 15 pages.

Savannah read 45 pages.

It took 15 minutes.

Step-by-step explanation:

To create a system of equations, we can model each set of given information using a linear equation:

$y=mx+b$

where:

• y represents the total number of pages read.
• x represents the time (in minutes) after the two classmates met.
• m represents the reading rate (in pages per minute).
• b represents the number of pages already read before the classmates met.

Given that Clarence's reading rate is 1 page per minute and he had already read 63 pages before meeting Savannah, then:

$y = x + 63$

Given that Savannah's reading rate is 3 pages per minute, and she had already read 33 pages before meeting Clarence, then:

$y=3x+33$

Therefore, we have created the following system of equations:

$\begin{cases}y = x + 63\\y=3x+33\end{cases}$

To determine the time at which the total number of pages they had read was the same, we can substitute the first equation into the second and solve for x:

$\begin{aligned}3x+33&=x+63\\\\3x+33-x&=x+63-x\\\\2x+33&=63\\\\2x+33-33&=63-33\\\\2x&=30\\\\\dfrac{2x}{2}&=\dfrac{30}{2}\\\\x&=15\end{aligned}$

Therefore, it took 15 minutes for them to have both read the same total number of pages.

To determine the number of pages each classmate read after they met, we can multiply the number of minutes (15) by their respective reading rates:

$\textsf{Clarence} = \textsf{1 page/min} \times \textsf{15 minutes} = \textsf{15 pages}$

$\textsf{Savannah} = \textsf{3 pages/min} \times \textsf{15 minutes} = \textsf{45 pages}$

So, after Clarence and Savannah met, it took 15 minutes of reading time until they had both read a total of 78 pages of their assigned History reading. In that time, Clarence read 15 pages and Savannah read 45 pages.