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 [tex]x[/tex] represent the number of days Allen has been reading. Then the number of days Mark has been reading is [tex](x+1)[/tex].
Mark is reading 40 pages per day. So, he will read [tex]40(x+1)[/tex] pages.
Allen is reading 45 pages a day. So, he will read [tex]45x[/tex] pages.
Allen catch up to Mark when they read equal number of pages.
[tex]40(x+1)=45x[/tex]
[tex]40x+40=45x[/tex]
[tex]40=45x-40x[/tex]
[tex]40=5x[/tex]
Divide both sides by 5.
[tex]\dfrac{40}{5}=\dfrac{5x}{5}[/tex]
[tex]8=x[/tex]
In 8 days Allen will catch up to Mark.
[tex]45x=45(8)[/tex]
[tex]45x=360[/tex]
Therefore, they each have read 360 pages.
