Work and Time calculation A is thrice as good as a workman as $B$ and therefore is able to finish a job in $60$ days less than $B$. How much time will they take to finish the same job if they work together?
My attempt:
Let's say that the amount of work done by $B$ in $1$ day = $1 \over B$
As $A$ is $3$ times better than $B$, hence the amount of work done by $A$ in $1$ day=$3 \over B$
The difference in times to complete the same work is $60$ days.
Hence, ${3 \over B} - {1 \over B} = {1 \over 60}$
Solving which gives me B as 120 days and A as 40 days. Working together, they can complete the same job in ${ 1 \over {1 \over 120} + {1 \over 40}}= 30$ days.
But the correct answer, as given in the question, is something else.
What did I do wrong?
 A: I learned how to do this with a table, so let's see if I can format it all correctly here. (Sorry in advance, my LaTex friends)
We know that rate (r)*time (t)=work, and that the work is the same for all jobs.
     Rate     Time      Work
A     3r      t-60        1 
  ------------------------- 
B     r       t           1
  ------------------------- 
Both  4r      ?           1


Now, we know that their rate together is 4r because rates can be added when they combine their abilities. If we set up a system:
   rt = 1
   3r(t-60) = 1
so
   3rt-180r = rt
   2rt = 180r
   t = 90 days
Then we can fill in our chart and figure out some other stuff.
     Rate     Time      Work
A     1/30     30       1 
  ------------------------- 
B     1/90(r)  90      1
  ------------------------- 
Both  4/90     x       1

Using again our equation:
   1 = 4x/90
   90/4 = x
   x= 45/2 days

That was a lot of formatting work, so please at least admire it if/when/before editing it. 
A: Let A takes $d$ days to complete the work, so B will take $3d$ days.
So, $3d-d=60\implies d=30$
So, A takes $30$ days , B takes $90$ days individually to complete the work.
So, A & B,together will do $\frac{1}{30}+\frac{1}{90}=\frac{2}{45}$ part of the whole work in one day.
So, together they will need $\frac{45}{2}$ days to complete the task. 
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A: Assume time speed of B is b and time taken is t and work is w 
b*t=w ....(1)
3b(t-60)=w...(2)
 by dividing (1) and (2)
2t=180
t=90 days
so there speed are w/30 work per dayand w/90 work per day
so while working together days to work
w/90+w/30=w/d
4/90=1/d
d=45/2
so total yime taken is 45/2 days
