Question

Elisabeth reads 15 of her book in 112 hours.

Elisabeth continues to read at this pace.

How long does it take Elisabeth to read 34 of the book?

Enter your answer as a mixed number in simplest form by filling in the boxes.

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Answer 1

To determine how long it takes Elisabeth to read 34 of the book, we first need to find her reading rate based on the information provided.

Elisabeth reads \( \frac{15}{112} \) of the book in 1 hour.

To find the time it takes to read \( \frac{34}{112} \) of the book, we can set up a ratio based on her reading rate.

Let \( t \) be the time in hours it takes to read \( \frac{34}{112} \) of the book. This gives us:

\[
\frac{34}{112} = \text{Rate} \times t
\]

We can express her reading rate as:

\[
\text{Rate} = \frac{15}{112} \text{ chapters per hour}
\]

Now, we need to find the amount of time:

\[
t = \frac{\frac{34}{112}}{\frac{15}{112}} = \frac{34}{112} \times \frac{112}{15} = \frac{34}{15}
\]

Now, we convert \( \frac{34}{15} \) into a mixed number.

First, we divide \( 34 \) by \( 15 \):

\[
34 \div 15 = 2 \quad \text{(with a remainder of 4)}
\]

Thus,

\[
\frac{34}{15} = 2 \frac{4}{15}
\]

Therefore, the time it takes Elisabeth to read \( \frac{34}{112} \) of the book, expressed as a mixed number in simplest form, is:

\[
\boxed{2 \frac{4}{15}}
\]

In the boxes:

- Hours: \(2\)
- Minutes: \(4/15\)