Official Solution:Jack can complete the task in 8 hours. Tom can complete the same task in 12 hours. If Jack works on the task alone for 4 hours and then Tom starts to help him, how many hours in total will Jack have worked by the time the task is finished?

A. 5.0

B. 5.2

C. 5.6

D. 6.4

E. 7.2

Since Jack can complete the task in 8 hours then in 4 hours that he works alone he does half of the task, so another half is has to be done. Combined rate of Jack and Tom working together is \(\frac{1}{8}+\frac{1}{12}=\frac{5}{24}\) task/hour, so working together they can complete the task in \(\frac{1}{(\frac{5}{24})}=\frac{24}{5}\) hours, which means that for half of the task they need another \(\frac{(\frac{24}{5})}{2}=\frac{24}{10}=2.4\) hours.

Hence, the total time that Jack worked is \(4+2.4=6.4\) hours.

Answer: D

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