John Empties a Barrel in 6 Days, Mary in 12 — Together?
John can drink an entire barrel of water by himself in 6 days. Mary can drink the same size barrel by herself in 12 days. If they start drinking from one barrel together, at the same time, how many days will it take the two of them to finish it?
Reveal the answer
4 days — not 9. The intuitive move is to average the two times, (6+12)/2 = 9, but combined work rates add rather than average: John drinks 1/6 of a barrel per day, Mary 1/12, so together they manage 1/6 + 1/12 = 1/4 per day, which empties the barrel in 4 days. It's one of four items Maggie Toplak, Richard West and Keith Stanovich added in 2014 to extend Shane Frederick's original three-question Cognitive Reflection Test.