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IMO Longlists
1984 IMO Longlists
51
51
Part of
1984 IMO Longlists
Problems
(1)
Two cyclists and a pedestrian in a circular runway
Source:
10/13/2010
Two cyclists leave simultaneously a point
P
P
P
in a circular runway with constant velocities
v
1
,
v
2
(
v
1
>
v
2
)
v_1, v_2 (v_1 > v_2)
v
1
,
v
2
(
v
1
>
v
2
)
and in the same sense. A pedestrian leaves
P
P
P
at the same time, moving with velocity
v
3
=
v
1
+
v
2
12
v_3 = \frac{v_1+v_2}{12}
v
3
=
12
v
1
+
v
2
. If the pedestrian and the cyclists move in opposite directions, the pedestrian meets the second cyclist
91
91
91
seconds after he meets the first. If the pedestrian moves in the same direction as the cyclists, the first cyclist overtakes him
187
187
187
seconds before the second does. Find the point where the first cyclist overtakes the second cyclist the first time.
algebra unsolved
algebra