Answer to Walking Track Quiz

 

Answer to Walking Track Quiz: https://hunterfiftyfour.blogspot.com/2025/11/walking-track-quiz.html

I measure my own lap time T_lap — the time I take to go once around the 1 km track.

I keep a record of the time t between two consecutive meetings with the other walker

The rule:

If t<1/2  T_lap ​ → I am slower

If t>1/2 T_lap →  I am faster.

If t=1/2  T_lap ​ → same speed.

Intuitively:

Between two successive meetings I always walk the same distance along the track. Call that distance ‘d’.

Now, this ‘d’ distance has contribution in terms of metres covered both by me and the other walker. If my contribution to ‘d’ is less than half the total loop – in this case 0.5 km – I am going slower. If mine and the other walker have equal contribution, we are going at same speed. If my contribution to ‘d’ is more, then I’m faster.

Translate this to time:

If ‘t’, the time between two consecutive meetings, is greater than half my lap time, then I’m slower than the other walker. If half my lap time is equal to ‘t’, then our speeds are equal. Else, my speed is more than the other walker’s speed.