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Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1965 AMC 12/AHSME
28
28
Part of
1965 AMC 12/AHSME
Problems
(1)
Escalator
Source:
1/11/2009
An escalator (moving staircase) of
n
n
n
uniform steps visible at all times descends at constant speed. Two boys,
A
A
A
and
Z
Z
Z
, walk down the escalator steadily as it moves,
A
A
A
negotiating twice as many escalator steps per minute as
Z
Z
Z
.
A
A
A
reaches the bottom after taking
27
27
27
steps while
Z
Z
Z
reaches the bottom after taking
18
18
18
steps. Then
n
n
n
is:
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
63
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
54
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
45
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
36
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
30
<span class='latex-bold'>(A)</span>\ 63 \qquad <span class='latex-bold'>(B)</span>\ 54 \qquad <span class='latex-bold'>(C)</span>\ 45 \qquad <span class='latex-bold'>(D)</span>\ 36 \qquad <span class='latex-bold'>(E)</span>\ 30
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
63
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
54
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
45
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
36
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
30