Over the summer break you went on a long trip and have pains

Over the summer break you went on a long trip and have painstakingly collected a 1,000 Gigabytes (1 Terabyte) worth of videos on your internet enabled camera. To avoid losing them, you\'d like to back the data up on to a computer at your home in prairie View. You have two options: Option A: Send the data over the internet to the computer in prairie view. The data rate for transmitting information across the internet from your hotel to prairie view is 1 megabyte per second. That\'s because you have decided to use the hotel\'s free WiFi in the lobby rather than paying for a more expensive in-room connection that guarantees you a minimum of 10 Megabytes per second. Option B: Copy the data over to a set of disks, which you can do at 100 Megabytes per second. Then rely on the US Postal Service to send the disks by mail, which takes 7 days. Which of these two options (A and B) is faster? And by how much? Option C: Suppose now you decide to splurge and choose to pay for the high speed connection at the hotel. Which option is faster now? And by now much?

Solution

Total data to be transmitted: 1000 Gigabytes = 1000 X 10^9 bytes

a. Rate of transmission - 1 megabyte per second = 10 ^6 bytes per sec which means 10^6 bytes would take 1 sec. Therefore 1000 X 10 ^9 bytes would take ( 1000X10^9)/ (10^6) = 1000X1000 sec.

No. of hours in a day = 24X60 X 60 sec = 86400 sec. Therefore, 1000 X 1000 sec are equivalent to 11.6 days

Hence it would take 11.6 days to transmit the data.

b. Rate of copying data: 100 megabytes per sec = 100 X 10 ^6 bytes per second.

The time that would be needed to copy 1000 gigabytes of data would be: ( 1000 X 10 ^ 9 ) / ( 100 X 10 ^ 6 ) = 10^4 sec

The no. of days that are equivalent to 10^4 sec = (10^4)/(86400) = 0.11days

The total time needed by second method would be : time needed to copy the data + postal service time = 0.11 + 7 = 7.11 days.

From the above, we can conclude that option B is faster ( since it takes 7.11 days when compared to option A which takes 11.6 days ). Option B is faster by 4.49 days.

c. The speed of high speed internet at hotel is : 10 mega bytes per sec.

To transmit 1000 Gigabytes, the time needed would be : (1000 X 10 ^9)/ ( 10 X 10^6 ) = 10 ^5 sec

This is equivalent to : ( 10 ^ 5) / 86400 = 1.15 days

Hence this is the fastest of all.