SOLUTION: Hi If Bob reads 25 pages a day he will need one more day to finish a book. If he reads 30 pages a day he will finish 2 days ahead of schedule. How many pages are there in the book

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Question 1209475: Hi
If Bob reads 25 pages a day he will need one more day to finish a book. If he reads 30 pages a day he will finish 2 days ahead of schedule. How many pages are there in the book.

Found 4 solutions by math_tutor2020, ikleyn, josgarithmetic, timofer:
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!

Answer: 450 pages

Explanation
Bob reading at some unknown pace was scheduled to finish the book by day number d.
Him reading at 25 pages per day means he needs an extra day. So he'll finish by day d+1.

25(d+1) = total number of pages = p

If Bob reads 30 pages per day, then he finishes 2 days ahead of schedule.
This means he takes d-2 days to read the same number of pages.
30(d-2) = p
30(d-2) = 25(d+1) ..... plug in p = 25(d+1)
30d-60 = 25d+25
30d-25d = 25+60
5d = 85
d = 85/5
d = 17
Bob needs d+1 = 17+1 = 18 days to read the entire book if the pace is 25 pages per day.
There are 25*18 = 450 pages in the book.

Answer by ikleyn(52772)   (Show Source):
You can put this solution on YOUR website!
.
If Bob reads 25 pages a day he will need one more day to finish a book.
If he reads 30 pages a day he will finish 2 days ahead of schedule.
How many pages are there in the book.
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        Here is another/different way to solve the problem.

Let P be the number of pages in the book. If Bob reads 25 pages per day, he needs days to finish reading. If Bob reads 30 pages per day, he needs days to finish reading. The difference is 1 + 2 = 3 days, according to the problem. So, we write this time equation - = 3 days. (1) It is your setup equation. To solve it, first multiply both sides by 150; then simplify 6P - 5P = 3*150 P = 450. At this point, the solution is complete. ANSWER. There are 450 pages in the book .

Solved.

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In this problems, 25 pages per day and 30 pages per day are the rates,
and equation (1) is the "time" equation.

So, the situation is a full analogue to Travel and Distance problems solved using a "time equation".

The total number of pages plays the role of the total one-way distance.

Answer by josgarithmetic(39615)   (Show Source):
You can put this solution on YOUR website!

RATE TIME PAGES 25 t+1 p 30 t-2 p

, expected 17 days to read the book.

, number of pages in the book

Answer by timofer(104)   (Show Source):
You can put this solution on YOUR website!
Maybe try to go directly to solve for number of pages.

reading rate time pages read 25 p/25 p p/x x p 30 p/30 p

From the description, the difference of how many days was 3.