Cable-laying teams X and Y together can lay a stretch in 9 days; teams Y and Z together can lay it in 12 days; teams X and Z together can lay it in 18 days. In how many days can all three teams lay the stretch working together?

Adding the three pair-rates: 1/9 + 1/12 + 1/18 = 4/36 + 3/36 + 2/36 = 1/4. Every team has been counted twice in that sum, so X + Y + Z = 1/8 of the stretch a day, giving 8 days. 4 days forgets to halve and treats 1/4 as the three-team rate. 39 days adds the day-counts 9 + 12 + 18, which adds times instead of rates. 13 days averages the three day-counts, which is not how rates combine either.