# 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?

• What have you tried so far? Is there any particular place you are getting stuck? – Michael Dyrud Aug 17 '15 at 19:27
• I am trying to find a formula for these particular type of questions. – Ali Haider Aug 17 '15 at 19:28
• But couldn't find yet – Ali Haider Aug 17 '15 at 19:28
• Please would u like to help. – Ali Haider Aug 17 '15 at 19:28
• Hint: How quickly can Asghar perform a job? In other words , how many jobs per day can he complete? – John Joy Aug 17 '15 at 22:41

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 $$\frac {60\times20}{60-20}=30$$

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 $$T_B = \frac1y = \ldots$$

• please explain how to find 3rd quantity – Ali Haider Aug 17 '15 at 19:41
• @AliHaider How far did you get with my hints? You should have the solution almost in front of you. Here it is generally required that you show some own work, so please try to solve the question yourself using the hint I gave. – AlexR Aug 17 '15 at 19:43
• ok thnx i got the solution – Ali Haider Aug 17 '15 at 19:44
• @AliHaider After you ask a question here, if you get an acceptable answer, you should "accept" the answer by clicking the check mark ✓ next to it. This scores points for you and for the person who answered your question. You can find out more about accepting answers here: How do I accept an answer?, Why should we accept answers?. – AlexR Aug 17 '15 at 19:58
• ok i have accepted sorry i didnt know that – Ali Haider Aug 17 '15 at 21:21