SOLUTION: One clerk can file 12 folders per minute and a second clerk, 9. How long will it take them working together to file 672 folders?

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Question 906942: One clerk can file 12 folders per minute and a second clerk, 9. How long will it take them working together to file 672 folders?
Found 4 solutions by northern, josmiceli, richwmiller, MathTherapy:
Answer by northern(3)   (Show Source):
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There might be a more logical way of doing it but i simply did guess and check
(12x20) + (9x20) = 420
(12x40) + (9x40) = 840
(12x30) + (9x30) = 630
(12x32) + (9x32) = 672
So it will take 32 minutes

Answer by josmiceli(19441)   (Show Source):
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In words, you need to find:
( the number of folders that need to be filed ) / ( their rate of filing them together )
---------------
The 1st clerk's rate of filing:
( 12 folders ) / ( 1 min )
The 2nd clerk's rate of filing:
( 9 folders ) / ( 1 min )
--------------------------
Add their rates of filing to
get their rate filing together:
Let = time in minutes
to file 1 folder

------------------------

-------------------
So, the rate working together is
and, you need:
( the number of folders that need to be filed ) / ( their rate of filing them together )

It will take them 32 minutes

Answer by richwmiller(17219)   (Show Source):
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Northern's method can be formulated.
(12x20) + (9x20) = 420
(12x40) + (9x40) = 840
(12x30) + (9x30) = 630
(12x32) + (9x32) = 672
So it will take 32 minutes
(12*t)+(9*t)=f
factor
t*(9+12)=f
add
t*21=f where f=672
substitute
t*21=672
solve
t=672/21
t=32
which is essentially what tutor josmiceli said in a more complicated way.

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

One clerk can file 12 folders per minute and a second clerk, 9. How long will it take them working together to file 672 folders?

Both file 9 + 12, or 21 folders in 1 minute
Then, with T being time taken, by both, to file 672, we form a proportion to get:

21T = 672 ------- Cross-multiplying
T, or time taken = , or minutes