The average download speed for Max's computer's Internet connection is 30 megabits per second. Assuming to interruptions in Internet service's, what is the best estimate for the maximum number of complete video files that Max can download to his computer in a six hour period if each video file if 4.2 gigabytes in size? (1 megabyte=8 megabits and 1 gigabyte=1,024 megabytes)

Options

A. `15`
B. `18`
C. `19`
D. `21`

Answer

To solve the problem step by step, follow these calculations:

### Step 1: Convert download speed from megabits to megabytes
Given:
- Download speed = 30 megabits per second
- 1 megabyte = 8 megabits

**Calculation:**
\[ \text{Download speed in megabytes} = \frac{30 \text{ megabits}}{8} = 3.75 \text{ megabytes per second} \]

### Step 2: Convert video file size from gigabytes to megabytes
Given:
- Size of each video file = 4.2 gigabytes
- 1 gigabyte = 1024 megabytes

**Calculation:**
\[ \text{Size of each video in megabytes} = 4.2 \text{ gigabytes} \times 1024 = 4300.8 \text{ megabytes} \]

### Step 3: Calculate the time taken to download one video file
Using the formula:
\[ \text{Time} = \frac{\text{Size of video}}{\text{Download speed}} \]

**Calculation:**
\[ \text{Time to download one video} = \frac{4300.8 \text{ megabytes}}{3.75 \text{ megabytes per second}} \approx 1146.88 \text{ seconds} \]

### Step 4: Convert the total time available from hours to seconds
Given:
- Total time = 6 hours
- 1 hour = 3600 seconds

**Calculation:**
\[ \text{Total time in seconds} = 6 \text{ hours} \times 3600 \text{ seconds/hour} = 21600 \text{ seconds} \]

### Step 5: Calculate the maximum number of complete video files that can be downloaded
Using the formula:
\[ \text{Number of videos} = \frac{\text{Total time available}}{\text{Time to download one video}} \]

**Calculation:**
\[ \text{Number of videos} = \frac{21600 \text{ seconds}}{1146.88 \text{ seconds}} \approx 18.83 \]

Since we can only download complete video files, we take the integer part:
\[ \text{Maximum number of complete videos} = 18 \]

### Final Answer:
Max can download a maximum of **18 complete video files** in a six-hour period.

---