Problem in time and work problems Asghar can do a job in 60 days. Both Asghar and Babar can do the same job in 20 day working together. How many days will it take Babar to do the job alone? The solution is 30 days. Is there a formula used to find this solution?
 A: Consider what fraction of the total job each person does in one day.
If person $A$ does the whole job in $x$ days, he does $\frac 1x$ of the job in one day.
If persons $A$ and $B$ together do the job in $y$ days, they do $\frac 1y$ of the whole job in one day.
On their own, person $B$ does $\frac 1y-\frac 1x$ of the job in one day, so the time it takes for them to do the whole job is $$\frac{1}{\frac 1y-\frac 1x}=\frac{xy}{x-y}$$
In this case, we have $$\frac {60\times20}{60-20}=30$$
A: Start like this:
A completes work at $x$ units / day. B completes work at $y$ units / day.
We are given the time A needs for one unit of work: $T_A = \frac1x$ and the amount of work A and B together need for one unit of work. We assume that they split the work "perfectly" so that their speeds add up: $z = x+y$, $T_{A+B} = \frac1z = \frac1{x+y}$. We ask for the time B needs for one unit of work ($T_B = \frac1y$).  
Plugging in gives you $y = z - x$ and $z = \frac1{T_{A+B}}$ and $x = \frac1{T_A}$. Combine this to
$$T_B = \frac1y = \ldots$$
