Time and Work Shortcut with examples

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  = $\frac { 1 }{ 5 }$

th part of whole work and

B’s 1 day’s work $\frac { 1 }{ 6 }$ th part of whole work

(A+B)’s one day’s work =$\frac { 1 }{ 5 } +\frac { 1 }{ 6 } =\frac { 11 }{ 30 } th$ part of whole work. so, both together will finish the work in

$\frac { 30 }{ 11 } days$=$2\frac { 8 }{ 11 }$

By Direct Formula

A+B can do the  work in $\frac { 5x6 }{ 5+6 } days=\frac { 30 }{ 11 } =2\frac { 8 }{ 11 }$

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$\frac { 1 }{ 8 }$ of the field.

In the second hour, Vishal mows $\frac { 1 }{ 12 }$ of the field

in the first two 2 hours $\frac { 1 }{ 8 } +\frac { 1 }{ 12 } =\frac { 5 }{ 24 }$ of the field is mown

In 8 hours $\frac { 5 }{ 24 } x4=\frac { 5 }{ 6 }$ of the field is mown

Now, $\left[ 1-\frac { 5 }{ 6 } \right] =\frac { 1 }{ 6 }$ of the field remains to be mown

in the 9th hour, vikar mows $\frac { 1 }{ 8 }$ of the field

Remaining work = $\frac { 1 }{ 6 } -\frac { 1 }{ 8 } =\frac { 1 }{ 24 }$

Vishal will finish the remaining work in $\left( { \frac { 1 }{ 24 } }/{ \frac { 1 }{ 12 } } \right)$

or  $\frac { 1 }{ 2 }$ of an hour

The total time required is $\left[ 8+1\frac { 1 }{ 2 } \right] or\quad 9\frac { 1 }{ 2 }$

Thus the work will be finished at $\left[ 8+1\frac { 1 }{ 2 } \right] or\quad 17\frac { 1 }{ 2 } \quad or\quad 5.30\quad pm$