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.

`(40)/(5)=(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.