This problem was posed in another thread:

Three runners start on the same spot of a circular track. They are called B,C and D. The ratio of their speeds is 3:5:7 respectively. We assume a constant speed around the track and they run in a clockwise fashion.

How many times will C and D lap B before they all meet up at the same point? Where is this first point of triple intersection?

Let's solve as best we can it using no math or programming, just with geogebra.

1)Use the circle with radius tool to draw a circle with the center at the origin and with a radius of 5. Color it a light brown.

2)Put 3 points on the circle called B,C and D.

3) Color them and enlarge to size 5.

4) Set the Algebra pane in object properties of B to
Cartesian coordinates.
increment .05
speed .3
repeat decreasing

5) Set the Algebra pane in object properties of C to
Cartesian coordinates.
increment .05
speed .5
repeat decreasing

6) Set the Algebra pane in object properties of D to
Cartesian coordinates.
increment .05
speed .7
repeat decreasing

7)Drag B,C and D to coordinates (0,5) and now hide the axes. Get this as accurate as possible by dragging or inputting the values. All 3 points should appear as one.

8)In the algebra pane select B,C and D, right click and click animation on.

The picture below shows that a triple intersection is about to occur at 180° from the start position. How many times did someone lap someone else?

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