John and David worked together and completed a piece of work in 30 days. John worked alone for 16 days and David alone completed the remaining part of the work in 44 days. In how much time could David alone complete the whole work?

Using the Least Common Multiple method, assume the total work is the Least Common Multiple of 30, 16, and 44, which is 2640 units. Their combined daily work is 2640 / 30 = 88 units. John works alone for 16 days and David finishes the rest in 44 days, so 16 * John's rate + 44 * David's rate = 2640. Since John's rate plus David's rate equals 88, multiplying this by 16 gives 1408 for 16 days of combined work, meaning David alone did the remaining 2640 - 1408 = 1232 units in 44 days. David's daily rate is 1232 / 44 = 28 units, so he alone takes 2640 / 28 = 60 days.

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