<PRE><B>Question 884691</B>
one man or 2 women or 3 boys can finish a job in 66 days.


the formula to use is:
R * P * T = Q
R = rate per person.
P = number of persons
T = time
Q = quantity of work.


set Q = 1 piece of work.
set T = 66
set P = the number of persons
you will want to solve for R which will give you the rate per person.


for the man:
R * P * T = Q becomes:
R * 1 * 66 = 1
divide both sides of this equation by 66 and you get:
R * 1 =  1/66
divide both sides of this equation by 1 to get:
R = 1/66
one man can finish 1/66 of the job in 1 day.


for the women:
R * P * T = Q becomes:
R * 2 * 66 = 1
divide both sides of this equation by 66 and you get:
R * 2 = 1/66
divide both sides of this equation by 2 to get:
R = 1/132
one woman can finish 1/132 of the job in 1 day.


for the boys:
R * P * T = Q becomes:
R * 3 * 66 = 1
divide both sides of this equation by 66 and you get:
R * 3 = 1/66
divide both sides of this equation by 3 to get:
R = 1/198
one boy can finish 1/198 of the job in 1 day.


the question is:
how many days will one man, one woman and one boy together take to finish the same work?


the rate of one man is 1/66
the rate of one woman is 1/132
the rate of 1 boy is 1/198


working together their rates are additive.


you get:


R * P * T = 1
Since P is equal to 1 all around, this formula becomes:
R * T = 1
The R in this case is the overall rate of the 3 people working together.
we get:
R = (1/66 + 1/132 + 1/198) which is equivalent to:
R = (6/396 + 3/396 + 2/396) which is equivalent to:
R = 11/396


R * T = 1 becomes:
11/396 * T = 1
divide both sidesof this eqution by (11/396) and you get:
T = 1 / (11/396) = 1 * (396/11) = 396/11 = 36 days.


1 man and 1 woman and 1 boy, working together, can complete the work in 36 days.



the man will have completed 1/66 * 36 = 36/66 of the work in 36 days.
the woman will have completed 1/132 * 36 = 36/132 of the work in 36 days.
the boy will have completed 1/198 * 36 = 36/198 of the work in 36 days.


add these up together and you should get 1.
36/66 + 36/132 + 56/198 is equivalent to:
(36*6 + 36*3 + 36*2) / 396 which is equivalent to:
(216 + 108 + 72) / 396 which is equivalent to:
396/396 which is equivalent to 1.


solution is correct.
answer is 36 days.






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