The students in Mrs. Reed's English class are reading the same $760$-page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in $20$ seconds, Bob reads a page in $45$ seconds and Chandra reads a page in $30$ 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 $1$ to a certain page and Bob will read from the next page through page $760,$ 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?

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Simon

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Today, 08:08

The students in Mrs. Reed's English class are reading the same $760$-page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in $20$ seconds, Bob reads a page in $45$ seconds and Chandra reads a page in $30$ 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 $1$ to a certain page and Bob will read from the next page through page $760,$ 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?

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Answers (1)

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Dominique Reed · Answer 1

456

Explanation:

Taking the number of pages Chandra reads as x; we formulate an equation:

In the equation below, 30 represents time taken by Chandra, 45 represents time taken by Bob and 760 is the number of pages in the novel.

Solving for x:

30x = 45 (760-x);

30x = 34,200 - 45x

30x + 45x = 34,200

75x = 34,200

x = 34,200 / 75

x = 456

Therefore Chandra will need to read up to the 456 page.