Tabular approach for solving Work problems

I found the below tabular approach useful and non-confusing, while solving the Work problems. Let me know what do you think and feel free to correct if i am wrong somewhere.

Problem 1:
Working, independently X takes 12 hours to finish a certain work. he finishes 2/3 of the work . The rest of the work is finished by Y whose rate is 1/10 th of X. In how much time does Y finsh his work?

Given:
X takes 12 hours to finish a certain work
X already finished 2/3 of the work
Y rate is 1/10th of X

Step1:
Since, X takes 12 hours to finish a certain work

	Time	Rate = work/Unit Time 1 HR
X	12	1/12
Y
X+Y

Step2: Y rate is 1/10th of X. Now the tabular form looks like:

	Time	Rate = work/Unit Time 1 HR
X	12	1/12
Y		(1/10) * (1/12) = 1/120
X+Y

Since, Y rate is 1/120 then the Y time is: 120 as below:

	Time	Rate = work/Unit Time 1 HR
X	12	1/12
Y	120	1/120
X+Y

Step3: X already finished 2/3 of work. So the left out work is 1/3

From the above table, If Y finishes 1/120 of work in 1 hr then
1/3 of work can be finished by Y in:
1/120 -----> 1 hr
1/3 -----> ??
(1/3)/(1/120) * 1 hr = 40 Hrs

****
Problem2:
Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?

A. 4
B. 6
C. 8
D. 10
E. 12

Given:
X takes 2 days longer to produce W widgets than machine Y
Two machine produce 5/4W widgets in 3 days

Step1:
X takes 2 days longer to produce W widgets than machine Y.
Assume Y takes n days to produce W widgets. Then,

	Time	Rate = work/Unit Time 1 day
X	n+2	1/(n+2)
Y	n	1/n
X+Y		((1/(n+2)) + (1/n))

In 1 day, X & Y finish ((1/(n+2)) + (1/n)) widgets
In 3 days, X & Y finish 3 * ((1/(n+2)) + (1/n)) widgets

But given,

3 * ((1/(n+2)) + (1/n)) = 5/3 ---> n = 4, n= -6/5 --> The only valid solution is, n = 4
Now substitute n=4 in the above table.

	Time	Rate = work/Unit Time 1 day
X	6	1/6
Y	4	1/4
X+Y		5/12

i.e., X takes 6 days to produce W widgets --> X takes 12 days to produce 2W widgets
****
Problem3:

Machine A and Machine B are used to manufacture 660 sprockets. It takes machine A ten hours longer to produce 660 sprockets than machine B. Machine B produces 10% more sprockets per hour than machine A. How many sprockets per hour does machine A produce?

Given:
Machine A and Machine B manufacture 660 sprockets.
A takes 10 hours longer than B
B produces 10% more per hour than A

Step1:
A takes 10 hours longer than B. Assume B takes N hours

	Time	Rate = work/Unit Time 1 HR
A	N+10	1/(N+10)
B	N	1/N
A+B

Step2:
B produces 10% more per hour than A
i.e., B rate = 1.1 Arate ==> 1/N = (1.1)*(1/(N+10)) ==> N = 100

Substitute N in the above table:

	Time	Rate = work/Unit Time 1 HR
A	110	1/110
B	100	1/100
A+B

Step3:

From the above table, 660 sprockets will be produced by A in 110 hours.
==> 6 sprockets for 1 hour.

****


Cheers!
Ravi