Question

Mark and Allen were assigned the same book to read for class. Mark started reading on Saturday , and he is reading 40 pages per day. Allen didn't start until Sunday , but he is still reading 45 pages a day.
How many days will it take Allen to catch up to Mark, and how many pages will they each have read?

Let x represent the number of days Allen has been reading.

Answer 1

Given:

Mark started reading on Saturday , and he is reading 40 pages per day.

Allen didn't start until Sunday , but he is still reading 45 pages a day.

To find:

How many days will it take Allen to catch up to Mark, and how many pages will they each have read?

Solution:

Let $x$ represent the number of days Allen has been reading. Then the number of days Mark has been reading is $(x+1)$.

Mark is reading 40 pages per day. So, he will read $40(x+1)$ pages.

Allen is reading 45 pages a day. So, he will read $45x$ pages.

Allen catch up to Mark when they read equal number of pages.

$40(x+1)=45x$

$40x+40=45x$

$40=45x-40x$

$40=5x$

Divide both sides by 5.

$\dfrac{40}{5}=\dfrac{5x}{5}$

$8=x$

In 8 days Allen will catch up to Mark.

$45x=45(8)$

$45x=360$

Therefore, they each have read 360 pages.