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Math  /  Numbers & Operations

QuestionDIO DEEPER You can read 12 pages of a book in 15 minutes. How many hours will it take you to read a 312 -page book?

Studdy Solution

STEP 1

1. You can read 12 12 pages in 15 15 minutes.
2. The book has 312 312 pages.
3. We need to determine the total time in hours to read the entire book.

STEP 2

1. Calculate the reading rate in pages per minute.
2. Calculate the total time in minutes to read the entire book.
3. Convert the total time from minutes to hours.

STEP 3

Calculate the reading rate in pages per minute.
Reading rate=12 pages15 minutes=45 pages per minute\text{Reading rate} = \frac{12 \text{ pages}}{15 \text{ minutes}} = \frac{4}{5} \text{ pages per minute}

STEP 4

Calculate the total time in minutes to read the 312 312 -page book.
Let t t be the total time in minutes.
t=312 pages45 pages per minutet = \frac{312 \text{ pages}}{\frac{4}{5} \text{ pages per minute}}

STEP 5

Solve for t t .
t=312×54=390 minutest = 312 \times \frac{5}{4} = 390 \text{ minutes}

STEP 6

Convert the total time from minutes to hours.
Total time in hours=390 minutes60 minutes per hour=6.5 hours\text{Total time in hours} = \frac{390 \text{ minutes}}{60 \text{ minutes per hour}} = 6.5 \text{ hours}
The total time to read the 312 312 -page book is:
6.5 hours\boxed{6.5 \text{ hours}}

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