A joint work problem

A piece of work was done by $A,B,C$; at first $A$ worked alone, but after some days was joined by $B$, and these two after some days were joined by $C$. The whole work could have been done by $B$ and $C$, if they had each worked twice the number of days that they actually did. The work could also have been completed without $B$'s help if $A$ had worked two-thirds and $C$ four times the number of days they actually did; or if $A$ and $B$ had worked together for 40 days without $C$; or if all three had worked together for the time that $B$ had worked. The number of days that elapsed before $B$ began to work was to the number that elapsed before $C$ began to work as 3 to 5: find the number of days that each man worked.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Miscellaneous Examples, No. 291