Question

Two classmates got together over the weekend to do their assigned History reading. Bobby can read 1 page per minute, while Rosa can read 4 pages per minute. When they met, Bobby had already read 32 pages, and Rosa had already gotten through 20 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:

In 4 minutes both have read 36 pages

Step-by-step explanation:

Let

x ----> the time in minutes

y ----> the number of pages read

we know that

The linear equation in slope intercept form is equal to

y=mx+b

where

m is the slope

b is the y-intercept

Bobby

The slope is

$m=1\ \frac{page}{minute}$

The y-intercept is

$b=32\ pages$ ----> initial value

so

$y=x+32$ ----> equation A

Rosa

The slope is

$m=4\ \frac{page}{minute}$

The y-intercept is

$b=20\ pages$ ----> initial value

so

$y=4x+20$ ----> equation B

Equate equation A and equation B

$4x+20=x+32$

solve for x

$4x-x=32-20\\3x=12\\x=4\ min$

For x=4 minutes

Bobby

$y=4+32=36\ pages$

Rosa

$y=4(4)+20=36\ pages$

therefore

In 4 minutes both have read 36 pages