Anandita and Bhuvaneshwari can finish reading a book in 5 hours and 6 hours respectively. They sit down to read their respective copies of the same book. They spend some time discussing the characters and in any hour, they could read, between the two of them, 21 pages less than what they would have read together, if they were not discussing. In 3 hours, the total number of pages read by them is equal to the number of pages in the book. How many pages are there in the book?
Question
Anandita and Bhuvaneshwari can finish reading a book in 5 hours and 6 hours respectively. They sit down to read their respective copies of the same book. They spend some time discussing the characters and in any hour, they could read, between the two of them, 21 pages less than what they would have read together, if they were not discussing. In 3 hours, the total number of pages read by them is equal to the number of pages in the book. How many pages are there in the book?
Solution
Let's break down the problem step by step:
- Anandita can finish reading a book in 5 hours, so her reading speed is 1 book/5 hours = 1/5 book per hour.
- Bhuvaneshwari can finish reading a book in 6 hours, so her reading speed is 1 book/6 hours = 1/6 book per hour.
- Together, if they were not discussing, they would read (1/5 + 1/6) book per hour = 11/30 book per hour.
- However, because they spend some time discussing, they read 21 pages less per hour. So, the number of pages they read per hour is (11/30 book per hour - 21 pages per hour).
- In 3 hours, the total number of pages read by them is equal to the number of pages in the book. So, the number of pages in the book is 3 * (11/30 book per hour - 21 pages per hour).
- To solve for the number of pages in the book, we need to convert the book per hour rate to a pages per hour rate. We can do this by setting up an equation where x is the number of pages in the book: 3 * (11/30*x - 21) = x.
- Solving this equation gives x = 315. So, there are 315 pages in the book.
Similar Questions
J.K. Rowling’s first book, Harry Potter and the Philosopher’sStone, is 225 pages long. Sam plans to read the book in three days,reading the same number of pages each day.a How many pages should Sam read each day?b The fraction 75225 of the book is equivalent to what fraction insimplest form?c By the end of the second day, Sam is on track and has read 23 ofthe book. How many pages of the book does 23 represent?
amar is reading a science fiction book for his book report project. He read 56 pages on Saturday and 45 pages on Sunday. How many pages did he read altogether?
I read 3/8 of a book on one day and 4/5 of the remainder on another day. If now there were 30 pages unread, the book contains:Options 240 pages 230 pages 340 pages 140 pages None of the above
Devin read a total of 154 pages over 14 hours. After a total of 41 hours of reading this week, how many pages will Devin have read in all? Assume the relationship is directly proportional.
The students in Mrs. Reed's English class are reading the same -page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in seconds, Bob reads a page in seconds and Chandra reads a page in seconds. Chandra and Bob, who each have a copy of the book, decide that they can save time by `team reading' the novel. In this scheme, Chandra will read from page to a certain page and Bob will read from the next page through page finishing the book. When they are through they will tell each other about the part they read. What is the last page that Chandra should read so that she and Bob spend the same amount of time reading the novel?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.