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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?

Respuesta :

calculista

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

[tex]m=1\ \frac{page}{minute}[/tex]

The y-intercept is

[tex]b=32\ pages[/tex] ----> initial value

so

[tex]y=x+32[/tex] ----> equation A

Rosa

The slope is

[tex]m=4\ \frac{page}{minute}[/tex]

The y-intercept is

[tex]b=20\ pages[/tex] ----> initial value

so

[tex]y=4x+20[/tex] ----> equation B

Equate equation A and equation B

[tex]4x+20=x+32[/tex]

solve for x

[tex]4x-x=32-20\\3x=12\\x=4\ min[/tex]

For x=4 minutes

Bobby

[tex]y=4+32=36\ pages[/tex]

Rosa

[tex]y=4(4)+20=36\ pages[/tex]

therefore

In 4 minutes both have read 36 pages

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