Alan can do a piece of work in 20 days, Bob in 28 days and Charlie in 24 days. All begin to do the work together, but Alan leaves after 5 days and Bob leaves 7 days before the completion of the work. How many days did the work last (approximately)?
Solution
Let the number of days the work lasted be $x$ days.
$\dfrac{5}{20} + \dfrac{x-7}{28} + \dfrac{x}{24} = 1$
$\dfrac{210 + 30x - 210 + 35x}{840} = 1$
$65x = 840$
$x = \dfrac{840}{65} = 12.92 \approx 13$ days