SOLUTION: The Department ot Education is holding their annual Brigada Eskwela to prepare and clean up the classrooms.Kimberly can paint a chair in 45 minutes.Arthur can paint the same chairs

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Question 1002869: The Department ot Education is holding their annual Brigada Eskwela to prepare and clean up the classrooms.Kimberly can paint a chair in 45 minutes.Arthur can paint the same chairs in 30 minutes. If they work together, how long will it take them to paint six chairs.
Found 6 solutions by mananth, ikleyn, n2, josgarithmetic, greenestamps, math_tutor2020:
Answer by mananth(16949) About Me  (Show Source):
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Painting the chair 1 job
Kimberly 45 minutes
She does 1/45 job in 1 minute
Arthur 30 minutes
He does 1/30 of thejob in 1 minute
Together they will do 1/45 + 1/30 +
Together they will do 1/18 of the job in one minute
So they will take 18 minutes

m.ananth@hotmail.ca

Answer by ikleyn(53744) About Me  (Show Source):
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.
The Department of Education is holding their annual Brigada Eskwela to prepare and clean up the classrooms.
Kimberly can paint a chair in 45 minutes. Arthur can paint the same highlight%28cross%28chairs%29%29 chair in 30 minutes.
If they work together, how long will it take them to paint six chairs.
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        The solution and the answer in the post by @mananth are catastrophically wrong.
        Trace attentively my solution below,  and you will find,  where @manant did his fatal error. 


The whole job is to paint 6 chairs (not one chair but six of them).


Kimberly can make this job in 30*6 = 180 minutes; hence, Kimberly makes 1/180 of the job per minute.

Arthur   can make this job in 45*6 = 270 minutes; hence, Kimberly makes 1/270 of the job per minute.


Working together, they make  

    1%2F180 + 1%2F270 = 3%2F540 + 2%2F540 = 5%2F540 = 1%2F108  of the job per minute.


Hence, they need 108 minutes, or 1 hour and 48 minutes to complete the job working together.      ANSWER

At this point, the problem is solved completely and correctly.



Answer by n2(78) About Me  (Show Source):
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.
The Department of Education is holding their annual Brigada Eskwela to prepare and clean up the classrooms.
Kimberly can paint a chair in 45 minutes. Arthur can paint the same highlight%28cross%28chairs%29%29 chair in 30 minutes.
If they work together, how long will it take them to paint six chairs.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 


The whole job is to paint 6 chairs (not one chair but six of them).


Kimberly can make this job in 30*6 = 180 minutes; hence, Kimberly makes 1/180 of the job per minute.

Arthur   can make this job in 45*6 = 270 minutes; hence, Kimberly makes 1/270 of the job per minute.


Working together, they make  

    1%2F180 + 1%2F270 = 3%2F540 + 2%2F540 = 5%2F540 = 1%2F108


of the job per minute.


Hence, they need 108 minutes, or 1 hour and 48 minutes to complete the job working together.    ANSWER

At this point, the problem is solved completely.



Answer by josgarithmetic(39791) About Me  (Show Source):
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                RATE              TIME         CHAIRS

Kimberly        1/45              45             1

Arthur          1/30              30             1

Combined       1/45+1/30           t            6

For the combined rate, the expression, best denominator to use should be 90.
2%2F90%2B3%2F90=5%2F90=highlight_green%281%2F18%29 when reduced.

%281%2F18%29t=6
t=18%2A6
highlight%28t=108%29

Answer by greenestamps(13326) About Me  (Show Source):
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All of the responses you have received so far use the same formal algebraic method that is found in most textbooks, using fractions of the job performed by each worker each minute.

Here is a less formal way of solving this kind of problem; this method can be a lot faster than the formal algebraic method, especially if the numbers are "nice".

Consider the least common multiple of the two given times, which is 90 minutes. In 90 minutes...
the number of chairs Kimberly can paint is 90/45 = 2
the number of chairs Arthur can paint is 90/3 = 3
the number of chairs they can paint together is 2+3 = 5

They can paint 5 chairs in 90 minutes, so the number of minutes it takes them to paint each chair is 90/5 = 18.

So the time required for them to paint 6 chairs is 18*5 = 108 minutes

ANSWER: 108 minutes

Answer by math_tutor2020(3835) About Me  (Show Source):
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Let's say for a hypothetical argument that each chair's surface area is 900 square inches.
As it turns out, this figure 900 doesn't matter since you can change it to any positive real number you want. The final answer at the end will remain the same.


Kimberly can paint one chair (900 square inches) in 45 minutes, so her unit rate is 20 square inches per minute because:
rate = amountDone/time = 900/45 = 20 square inches per minute


Meanwhile,
Arthur's unit rate = 900/30 = 30 square inches per minute

When the two work together, the combined unit rate would be 20+30 = 50 square inches per minute.
This assumes neither person slows the other down.

1 chair has 900 square inches of material.
6 chairs cover 6*900 = 5400 square inches

rate*time = amountDone
time = amountDone/rate
time = 5400/50
time = 108 minutes
time = 60 min + 48 min
time = 1 hr + 48 min


Answer: 108 minutes (i.e. 1 hour & 48 minutes)

Side note: The answer by mananth applies to 1 chair. You have to multiply 18 by 6 to get the time duration for 6 chairs.