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Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1954 AMC 12/AHSME
30
30
Part of
1954 AMC 12/AHSME
Problems
(1)
Doing a Job Together and Alone
Source:
2/7/2009
A
A
A
and
B
B
B
together can do a job in
2
2
2
days;
B
B
B
and
C
C
C
can do it in four days; and
A
A
A
and
C
C
C
in
2
2
5
2\frac{2}{5}
2
5
2
days. The number of days required for
A
A
A
to do the job alone is:
<
s
p
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c
l
a
s
s
=
′
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a
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x
−
b
o
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>
(
A
)
<
/
s
p
a
n
>
1
<
s
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c
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a
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=
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x
−
b
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>
(
B
)
<
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p
a
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>
3
<
s
p
a
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c
l
a
s
s
=
′
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x
−
b
o
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>
(
C
)
<
/
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a
n
>
6
<
s
p
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c
l
a
s
s
=
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a
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e
x
−
b
o
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′
>
(
D
)
<
/
s
p
a
n
>
12
<
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p
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c
l
a
s
s
=
′
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x
−
b
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′
>
(
E
)
<
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>
2.8
<span class='latex-bold'>(A)</span>\ 1 \qquad <span class='latex-bold'>(B)</span>\ 3 \qquad <span class='latex-bold'>(C)</span>\ 6 \qquad <span class='latex-bold'>(D)</span>\ 12 \qquad <span class='latex-bold'>(E)</span>\ 2.8
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
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d
′
>
(
A
)
<
/
s
p
an
>
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
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′
>
(
B
)
<
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p
an
>
3
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
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d
′
>
(
C
)
<
/
s
p
an
>
6
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
12
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
2.8