meeting-time-piecewise-rate
Two or more travelers move along a shared route with piecewise-constant speeds (or with discrete schedules like stops and waits). Find when or where they meet, board, pass, or are at the same position. The decisive move is identifying the segments where each traveler's rate is constant and using "closing-speed × time = gap" or a side-by-side schedule table rather than a single algebraic equation.
How to solve
- Swap one traveler's continuous-rate leg for a 'stops every N min' discrete schedule — the simulation table cleanly handles both
- Introduce a midpoint speed change (e.g. faster on the return trip) to force two-segment reasoning per traveler
- For an easier Gr5 variant use integer-only meeting times; reserve fractional/decimal meet points for Gr6+ variants
Sub-archetype mix (3)
Click a row to see member problems.
- constant-rate-closing-speed 41% (12)
Two travelers move toward or past each other at one constant speed each; the decisive move is computing relative (closing or passing) speed — sum of speeds if head-on, difference if same-direction — then dividing the relevant distance by that combined rate to find meeting time, meeting position, or visibility duration.
- piecewise-leg-time-balance 41% (12)
One or more travelers have two or more constant-speed legs separated by a landmark or route boundary; the decisive move is summing the time fractions for each leg and equating total travel time across travelers, or solving for an unknown second-leg speed given a fixed time budget.
- staggered-start-schedule-table 17% (5)
One party starts later, joins mid-task at an unknown time, or follows a discrete repeating schedule (e.g., drive N minutes then wait M minutes per stop); the decisive move is building a side-by-side time table or working backwards from a known end-time to locate when the staggered event began.
More data (year-over-year, tool fingerprint, grade distribution, all members)
Tool fingerprint (1–17)
Grade distribution
- Gr 5 2
- Gr 6 14
- Gr 7 10
- Gr 8 3