To return the book to the library in time the student had to read 40 pages every day, but he read 15 pages less a day and returned the book 6 days late. In how many days was the student supposed to read the book?

He was supposed to read the book in 10 days.

Step-by-step explanation:

Let d = number of days he should have taken to read the book.

He should have read 40 pages per day for d days. That means 40d number of pages.

He read 15 pages per day less than he should have, so he read 40 - 15 = 25 pages per day. He took an extra 6 days, so he took d + 6 number of days. Reading 25 pages per day for d + 6 days, he read a total of 25 (d + 6) pages.

The number of pages of the book is the same either way, so

40d = 25 (d + 6)

40d = 25d + 150

15d = 150

d = 10

Answer: He was supposed to read the book in 10 days.

Check:

He should have done this: 10 days at 40 pages/day = 400 pages.

He did this: 40 - 15 = 25 pages/day; 10 days + 6 days = 16 days.

16 days at 25 pages/day = 400 pages.

Since we get the same number of pages both ways, the answer is correct.