A puzzle by Pierre Berloquin:
Timothy, Urban, and Vincent are digging identical holes in a field.
- When Timothy and Urban work together, they dig 1 hole in 4 days.
- When Timothy and Vincent work together, they dig 1 hole in 3 days.
- When Urban and Vincent work together, they dig 1 hole in 2 days.
Working alone, how long does it take Timothy to dig one hole?
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In one day:
- Timothy and Urban dig 1/4 hole.
- Timothy and Vincent dig 1/3 hole.
- Urban and Vincent dig 1/2 hole.
If we made a clone of Timothy and set all four workers digging for one day, they’d dig 1/4 + 1/3 = 7/12 hole.
Since Urban and Vincent working together dig 6/12 hole per day, Timothy and his clone dig 1/12. So Timothy alone digs 1/24 hole per day, and can dig one hole in 24 days.
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