Agent Hunt transferred classified files from the CIA mainframe onto his flash drive. The drive had some files on it before the transfer, and the transfer happened at a rate of 4.4 megabytes per second. After 32 seconds, there were 384 megabytes on the drive. The drive had a maximum capacity of 1000 megabytes.
How full was the drive when the transfer began?
How long from the time that Agent Hunt started the transfer did it take the drive to be completely full?

Okay so we know that the files were transferred at a rate of 4.4 megabytes per second and with that we can say that 4.4T megabytes were transferred in T seconds.

The size of the files on the drive is comprised of the files that were on the drive before the transfer began and the files that were transferred. We can express this with the equation S=A+4.4T in which S represents the size of the files on said drive at a given amount of time, A represents the size of the files before the transfer began, and T represents the time (in seconds).

We want to find A, so let's solve the equation for A first which is:

S=A+4.4T now turns into A=S-4.4T

So now we know that after 32 seconds (T=32), there were 384 megabytes on the drive (S=384). Now let's plug these values into the equation to find the value of A.

A= 384-4.4*32= 243.2

So the answer is when the transfer began, the drive had 243.2 megabytes on it.

But to find how long it took the drive to be completely full, we need to plug in S=1000 into the equation and solve for T.

243.2=1000-4.4T

4.4T=756.8

T=172

Hopefully this helps!

joaobezerra joaobezerra · Answer 2 · 2021-08-10T21:43:54+02:00

This question is solved by proportions.

According to the data given, first we find the load of the drive when the transfer began.
Then, it the time it takes for the drive to be full can be found.

With this, we find that:

Initially, the drive had 243.2 megabytes.
It will take 172 seconds for the drive to be completely full.

We have that:

After 32 seconds, there are 384 megabytes.
Rate of of 4.4 megabytes per second.

How full was the drive when the transfer began?

For each of the 32 seconds, we remove 4.4 megabytes, considering that there are 384 megabytes, so:

[tex]384 - 32*4.4 = 243.2[/tex]

Initially, the drive had 243.2 megabytes.

How long from the time that Agent Hunt started the transfer did it take the drive to be completely full?

Rate of 4.4 megabytes per second.
To insert 1000 - 243.2 = 756.8 megabytes.

Applying the rule of three:

1 second - 4.4 MB

x seconds - 756.8 MB

Applying cross multiplication:

[tex]4.4x = 756.8[/tex]

[tex]x = \frac{756.8}{4.4}[/tex]

[tex]x = 172[/tex]

It will take 172 seconds for the drive to be completely full.

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