# A document with a volume of 5 MB can be transferred from one computer to another in two ways

A document with a volume of 5 MB can be transferred from one computer to another in two ways: A) Compress by an archiver, transfer the archive via a communication channel, unpack B) Transfer via a communication channel without using an archiver Which method is faster if the average data transfer rate through the communication channel is 2 ^ 18 bits per second, – the volume of the document compressed by the archiver is equal to 20% of the original, – the time required for compressing the document – 7 seconds, for unpacking – 1 second? In the answer, write the letter A if method A is faster or B if method B is faster. Immediately after the letter, write the number of seconds, how much faster one method is than the other.

Uncompressed file size in bits:

V = 5 MB * 8 bits / byte * 2 ^ 20 bytes / MB = 5 * 2 ^ 3 * 2 ^ 20 = 5 * 2 ^ 23 bits.

Compressed file size:

Va = 5 MB * 0.20 = 1 MB.

Compressed file size in bits:

Va = 1 * 2 ^ 23 bits.

Uncompressed document transmission time: t = 5 * 2 ^ 23 bits / 2 ^ 18 bits / s = 5 * 2 ^ 5 s = 5 * 32 s = 160 s.

Compressed file transfer time: ta = 2 ^ 23 bits / 2 ^ 18 bits / s = 2 ^ 5 s = 32 s.

Archiving time + decompression time: 7 s + 1 s = 8 s.

Total for transferring a compressed file: 32 s + 8 s = 40 s.

File transfer time difference: 160 s – 40 s = 120 s 