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May Olympiad
May Olympiad L1 - geometry
1995.5
1995.5
Part of
May Olympiad L1 - geometry
Problems
(1)
tortoise and lizard walk around a rectangle
Source: I May Olympiad (Olimpiada de Mayo) 1995 L1 P5
9/17/2022
A tortoise walks
60
60
60
meters per hour and a lizard walks at
240
240
240
meters per hour. There is a rectangle
A
B
C
D
ABCD
A
BC
D
where
A
B
=
60
AB =60
A
B
=
60
and
A
D
=
120
AD =120
A
D
=
120
. Both start from the vertex
A
A
A
and in the same direction (
A
→
B
→
D
→
A
A \to B \to D \to A
A
→
B
→
D
→
A
), crossing the edge of the rectangle. The lizard has the habit of advancing two consecutive sides of the rectangle, turning to go back one, turning to go forward two, turning to go back one and so on. How many times and in what places do the tortoise and the lizard meet when the tortoise completes its third turn?
geometry
algebra
rectangle