In the afternoon , a student read 100 pages at the rate of 60 pages/h . In the evening , when she was tired she read 100 more pages at the rate of 40 pages/h . What was her average rate of reading, in pages per hour ?

Options

A. 48
B. 50
C. 60
D. 70

Answer

To find the average rate of reading, we need to determine the total number of pages read and the total time spent reading.

### Step 1: Calculate the time spent reading in the afternoon
The student read 100 pages at a rate of 60 pages per hour.

\[ \text{Time in afternoon} = \frac{\text{Pages}}{\text{Rate}} = \frac{100 \text{ pages}}{60 \text{ pages/hour}} = \frac{100}{60} \text{ hours} = \frac{5}{3} \text{ hours} \approx 1.67 \text{ hours} \]

### Step 2: Calculate the time spent reading in the evening
The student read another 100 pages at a rate of 40 pages per hour.

\[ \text{Time in evening} = \frac{\text{Pages}}{\text{Rate}} = \frac{100 \text{ pages}}{40 \text{ pages/hour}} = \frac{100}{40} \text{ hours} = 2.5 \text{ hours} \]

### Step 3: Calculate the total time spent reading
Now, we add the time spent in the afternoon and the evening:

\[ \text{Total time} = \text{Time in afternoon} + \text{Time in evening} = \frac{5}{3} \text{ hours} + 2.5 \text{ hours} \]

To add these, convert 2.5 hours into a fraction:

\[ 2.5 \text{ hours} = \frac{5}{2} \text{ hours} \]

Now, find a common denominator (which is 6):

\[ \frac{5}{3} = \frac{10}{6}, \quad \frac{5}{2} = \frac{15}{6} \]

So,

\[ \text{Total time} = \frac{10}{6} + \frac{15}{6} = \frac{25}{6} \text{ hours} \]

### Step 4: Calculate the total number of pages read
The total number of pages read is:

\[ \text{Total pages} = 100 \text{ pages (afternoon)} + 100 \text{ pages (evening)} = 200 \text{ pages} \]

### Step 5: Calculate the average rate of reading
The average rate of reading is given by:

\[ \text{Average rate} = \frac{\text{Total pages}}{\text{Total time}} = \frac{200 \text{ pages}}{\frac{25}{6} \text{ hours}} = 200 \times \frac{6}{25} = \frac{1200}{25} = 48 \text{ pages/hour} \]

### Final Answer
The average rate of reading is **48 pages per hour**.

---