Time and Work
A can do a piece of work in 5 days, and B can do it in 6 days. How long will they take if both work together?
A’s 1 day’s work =
B’s 1 day’s work 
(A+B)’s one day’s work =
By Direct Formula
A+B can do the work in
Two men, Vikas and Vishal, working separately can mow a field in 8 and 12 hours respectively. If they work in stretches of one hour alternately, Vikas beginning at 8 a.m, when will the mowing be finished?
In the first hour, Vikas mows
In the second hour, Vishal mows 
in the first two 2 hours 
In 8 hours 
Now, ![\left[ 1-\frac { 5 }{ 6 } \right] =\frac { 1 }{ 6 }](https://s0.wp.com/latex.php?latex=%5Cleft%5B+1-%5Cfrac+%7B+5+%7D%7B+6+%7D+%C2%A0%5Cright%5D+%3D%5Cfrac+%7B+1+%7D%7B+6+%7D+&bg=ffffff&fg=000&s=0&c=20201002 "\left[ 1-\frac { 5 }{ 6 } \right] =\frac { 1 }{ 6 }")
in the 9th hour, vikar mows
Remaining work =
Vishal will finish the remaining work in
or 
The total time required is
![\left[ 8+1\frac { 1 }{ 2 } \right] or\quad 9\frac { 1 }{ 2 }](https://s0.wp.com/latex.php?latex=%5Cleft%5B+8%2B1%5Cfrac+%7B+1+%7D%7B+2+%7D+%C2%A0%5Cright%5D+or%5Cquad+9%5Cfrac+%7B+1+%7D%7B+2+%7D+&bg=ffffff&fg=000&s=0&c=20201002 "\left[ 8+1\frac { 1 }{ 2 } \right] or\quad 9\frac { 1 }{ 2 }")
Thus the work will be finished at
![\left[ 8+1\frac { 1 }{ 2 } \right] or\quad 17\frac { 1 }{ 2 } \quad or\quad 5.30\quad pm](https://s0.wp.com/latex.php?latex=%5Cleft%5B+8%2B1%5Cfrac+%7B+1+%7D%7B+2+%7D+%C2%A0%5Cright%5D+or%5Cquad+17%5Cfrac+%7B+1+%7D%7B+2+%7D+%5Cquad+or%5Cquad+5.30%5Cquad+pm&bg=ffffff&fg=000&s=0&c=20201002 "\left[ 8+1\frac { 1 }{ 2 } \right] or\quad 17\frac { 1 }{ 2 } \quad or\quad 5.30\quad pm")
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