Problema Solution

Alice can decrypt 3 files in twice as long as Bob can decrypt 1 file. It takes Charlie 3 hours longer to decrypt 1 file than it takes Bob to decrypt a file. If Alice, Bob, and Charlie all work together, it takes them 16 hours to decrypt 10 files. How long does it take Bob to decrypt 1 file by himself?

Answer provided by our tutors

Let

x = the hours Bob needs to decrypt 1 file by himself

1/x filer per hour is Bob's rate

3/2x files per hour is Alice's rate

x + 3 = the hours Charlie needs to decrypt 1 file by himself

1/(x + 3) files per hour is Charlie's rate

The together rate is 10/16 file per hour or 5/8 file per hour.

1/x + 3/(2x) + 1/(x + 3) = 5/8

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click here to see the equation solved for x

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x = 5 hr

We need to ignore the negative solution - 2.4 since the time of encrypting can only be positive.

Bob needs 5 hours to decrypt 1 file by himself.