To determine the memory space needed to electronically house the 39 million books in the Library of Congress, we will start by using the given information and apply fraction multiplication.

First, establish the relationship given:

• 1 book (500 pages) = 1 megabyte (MB)

We need to find the total memory space for 39 million books.

Let's denote:

• $N$ = 39,000,000 books
• Memory space required per book = 1 MB

Now, multiply the number of books by the memory space required for each book:

$\text{Total memory space} = N \times 1 \, \text{MB}$ $\text{Total memory space} = 39,000,000 \, \text{MB}$

Thus, the memory space needed to house 39 million books is 39,000,000 megabytes.

Next, we need to find out how long it would take to upload all of the eBooks of the Library of Congress onto a server at an upload rate of 29.3 megabits per second (Mbps).

First, convert the total memory space from megabytes (MB) to megabits (Mb):

• 1 megabyte (MB) = 8 megabits (Mb)

$\text{Total memory space in megabits} = 39,000,000 \, \text{MB} \times 8 \, \text{Mb/MB}$ $\text{Total memory space in megabits} = 312,000,000 \, \text{Mb}$

Now, we need to determine the time taken to upload this total memory space at a rate of 29.3 Mbps:

$\text{Time} = \frac{\text{Total memory space in megabits}}{\text{Upload rate}}$ $\text{Time} = \frac{312,000,000 \, \text{Mb}}{29.3 \, \text{Mbps}}$

$\text{Time} \approx 10,650,171 \, \text{seconds}$

Convert this time into more reasonable units (hours, days, years):

$\text{Time in hours} = \frac{10,650,171 \, \text{seconds}}{3600 \, \text{seconds/hour}}$ $\text{Time in hours} \approx 2,958.38 \, \text{hours}$

$\text{Time in days} = \frac{2,958.38 \, \text{hours}}{24 \, \text{hours/day}}$ $\text{Time in days} \approx 123.27 \, \text{days}$

Therefore, it would take approximately 123.27 days to upload all of the eBooks of the Library of Congress onto a server at a rate of 29.3 Mbps.

Would you like any more details or have any questions about this?

Here are some additional questions related to this topic:

1. How would the required memory space change if the average number of pages per book increased to 600 pages?
2. What would be the upload time if the upload rate doubled to 58.6 Mbps?
3. If the upload rate was reduced to 14.65 Mbps, how long would it take to upload all the books?
4. How much storage space in terabytes (TB) would be required for the 39 million books?
5. What if only half of the books in the Library of Congress needed to be uploaded? How long would it take then?

Tip: To quickly convert large time values, remember that there are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day. This helps in converting seconds to more practical units like minutes, hours, and days.