Ganga and Saraswati, working separately can mow field in 8 and 12 hours respectively. If they work in stretches of one hour alternately. Ganga is beginning at 9 a.m., when will the moving be completed?

According to question,
Ganga begins at 9 am and she does 3 units/hours
Saraswati begins at 10 am and she does 2 units/hours
So by 11 am they complete 5 units
Time $$ = \frac{{{\text{T}}{\text{.W}}.}}{{3 + 2}} = \frac{{24}}{5}$$
(4 cycle of 2 hrs each + 4 units left)
And now ganga will complete 3 unit out of 4 units in 1 hr
Now, rest 1 unit work done by = $$\frac{1}{2}$$ hr
Total time = 8 + 1 + $$\frac{1}{2}$$ = 9$$\frac{1}{2}$$ hr
Hence, Work finished at
= 9 am + 9$$\frac{1}{2}$$ hr
= 6:30 PM

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Alternate Solution:
Work done by Ganga in 1 hour = $$\frac{1}{8}$$
Work done by Saraswati in 1 hour = $$\frac{1}{12}$$
They are working alternatively with Ganga beginning the job.
Work done in every two hours = $$\frac{1}{8}$$ + $$\frac{1}{12}$$ = $$\frac{5}{24}$$
Work done in 4 × 2 = 8 hours = $$\frac{5\times4}{24}$$ = $$\frac{5}{6}$$
Remaining work = 1 - $$\frac{5}{6}$$ = $$\frac{1}{6}$$
In 9th hour, Ganga starts the work and does $$\frac{1}{8}$$ of the work
Work remaining = $$\frac{1}{6}$$ - $$\frac{1}{8}$$ = $$\frac{1}{24}$$
In 10th hour, Saraswati starts the work
Time needed to finish the remaining work
$$\eqalign{ & = \frac{{\frac{1}{{24}}}}{{\frac{1}{{12}}}} \cr & = \frac{1}{{24}} \times 12 \cr} $$
  $$=$$ 0.5 hours
  $$=$$ 30 minutes
i.e., work will be completed in 9 hour 30 minutes, after 9 AM
i.e., at 6:30 PM