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

In 4 minutes both have read 36 pages

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\ (page)/(minute)`

The y-intercept is

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

so

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

Rosa

The slope is

`m=4\ (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