Question

Richard can read 1/4 of a book in 2/5 of an hour. At this rate, how much can Richard read in one hour?
A.
1/10 of a book

B.
5/8 of a book

C.
1 3/5 books

D.
1/3 of a book

Answer 1

Richard can read \( \frac{1}{4} \) of a book in \( \frac{2}{5} \) of an hour.

To find out how much Richard can read in one hour, we need to find the rate at which he reads and then extrapolate that to one hour.

If Richard reads \( \frac{1}{4} \) of a book in \( \frac{2}{5} \) of an hour, we can find the reading rate per hour by setting up a proportion:

1. First, determine how many of those \( \frac{2}{5} \) hour intervals fit into 1 hour.

\[
\text{Number of intervals in 1 hour} = \frac{1 \text{ hour}}{\frac{2}{5} \text{ hour}} = 1 \cdot \frac{5}{2} = \frac{5}{2} = 2.5 \text{ intervals}
\]

2. Now, since he reads \( \frac{1}{4} \) of a book in \( \frac{2}{5} \) of an hour, in one hour he can read:

\[
\text{Books read in 1 hour} = 2.5 \cdot \frac{1}{4} = \frac{2.5}{4} = \frac{2.5 \cdot 1}{4} = \frac{2.5}{4} = \frac{2.5}{4} = \frac{2.5 \cdot 1}{4 \cdot 1} = \frac{2.5}{4}
\]

3. To calculate \( \frac{2.5}{4} \):

\[
\frac{2.5}{4} = \frac{25}{40} = \frac{5}{8}
\]

Thus, Richard can read \( \frac{5}{8} \) of a book in one hour.

The answer is **B. \( \frac{5}{8} \) of a book.**