Greek Anthology Book XIV: 7. - Problem/Variant/Mistake

Source Work

1992: David Wells: Curious and Interesting Puzzles:

The Puzzles:

Light Reflected off a Mirror: $20$

Solution

Mistake

$A$ and $B$ together can do a piece of work in $6$ days, $B$ and $C$ together in $20$ days, $C$ and $A$ together in $7 \frac 1 2$ days. How long will each require separately to do the same work?

The solution is given as:

$A$, $B$ and $C$ do the whole job in $10$, $15$ and $30$ days respectively.

Correction

With the numbers given, the results are actually:

$A$, $B$ and $C$ do the whole job in $8$, $24$ and $120$ days respectively.

For the given solution to be correct, it would be necessary for the question to have been:

$A$ and $B$ together can do a piece of work in $6$ days, $B$ and $C$ together in $10$ days, $C$ and $A$ together in $7 \frac 1 2$ days. How long will each require separately to do the same work?

(Emphasis added.)

One of the following things has happened:

$(1): \quad$ There is an error in the source work, and David Wells has reported it as it has been printed.

$(2): \quad$ The source work is correct, but a typo has been introduced into the question when it was entered into Curious and Interesting Puzzles.

It has not been possible to check the source work The Tutorial Arithmetic, 3rd ed. by W.P. Workman to determine which is the case.

Sources

• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): Light Reflected off a Mirror: $20$