Length of the track

Geometry Level 2

Ana and Bia walk along a circular track with constant velocities, starting from the same point, at the same moment, but in opposite directions. The first encounter between them is 48 meters to the left and the second encounter 20 meters to the right of the start. What is the total length of the track?


The answer is 116.

Luiz Claudio by Luiz Claudio , 19, Brazil

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1 solution

From the perspective of the person walking to the left, they will have walked to the left a total of 2 × 48 = 96 2 \times 48 = 96 meters at the time of the second encounter, at which point they would need to walk another 20 20 meters to return to the starting point. Thus the total length of the track is 96 + 20 = 116 96 + 20 = \boxed{116} meters.

1 Helpful 0 Interesting 2 Brilliant 0 Confused

What does "left" mean? I could think of two ways of defining it:

1) "Left" and "right" refer to movement along the circumference, either clockwise or counterclockwise. In other words, the problem universe is 1D with weird wrapping properties.

2) "Left" and "right" refer to projections from the circle onto the Cartesian axes.

I was reluctant to try it because of this ambiguity

Steven Chase - 2 years, 3 months ago

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I had some reluctance too initially, but option 1) seemed the most likely so I assumed that definition. It would probably be better if Luiz changed "left/right" to "clockwise/counterclockwise" for sake of clarity.

Brian Charlesworth - 2 years, 3 months ago

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Maybe we can post a follow up with left and right defined in Cartesian terms

Steven Chase - 2 years, 3 months ago

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