SOLUTION: If one man or two women or three boys can finish a work in 66days then how many days will one man, one woman and one boy together take to finish the same work?

Question 884691: If one man or two women or three boys can finish a work in 66days then how many days will one man, one woman and one boy together take to finish the same work?
Found 3 solutions by josmiceli, Theo, MathTherapy:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = the rate that a man works
Let = the rate that a woman works
Let = the rate that a boy works
( the rates are in jobs / day )
------------------------------------
(1)
(2)
(3)
--------------------
(1)
(2)
(3)
---------------------
Let = days to finish the job
Add their rates of working to get
their rate working together

Multiply both sides by

One man, one woman and one boy will
finish the job in 11 days

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
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.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

If one man or two women or three boys can finish a work in 66days then how many days will one man, one woman and one boy together take to finish the same work?

Since 1 man can do the work in 66 days, he can do of work in 1 day
Since 2 women can do the work in 66 days, then 1 woman can do work in 2(66), or 132 days, or of work in 1 day
Since 3 boys can do the work in 66 days, then 1 boy can do work in 3(66), or 198 days, or of work in 1 day
Therefore, with T being time it�ll take 1 man, 1 woman, and 1 boy, we have:

6T + 3T + 2T = 396 ------- Multiplying by LCD, 396T
11T = 396 ------- Cross-multiplying
T, or time taken by 1 man, 1 woman, and 1 boy to complete the work = , or days
You can do the check!!
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