Worked solution
Combine a capped geometric plan with arithmetic increments
A student with a knee problem plans swimming and jogging to prepare for a 2.4 km NAPFA run. On day 1 he jogs m and swims m. From day 2, jogging rises by of the previous day’s distance but is capped at m per day; swimming increases by m each day. Find the combined distance after 20 days, and the first day his combined daily distance reaches km.
[2012/PJC/Promo/8]
CJC · Discussion · Question 17
Answer
Combined 20-day distance m; first km day is day 37.
Apply the cap at the correct day
The printed daily pattern is:
| Day | Jog (m) | Swim (m) |
|---|---|---|
| 1 | 200 | 200 |
| 2 | 240 | 250 |
| 3 | 288 | 300 |
| 4 | 345.6 | 350 |
| 5 | 400 (cap) | 400 |
The uncapped fifth jog would exceed 400, so only days 1–4 use the GP; days 5–20 give sixteen capped jogs.
Sum each activity without rounding exact distances
Swimming totals m. Jogging totals m. The exact combined total is m; the printed note correctly says not to round this exact value to 3 significant figures.
Find the first qualifying daily distance
After day 4 the daily jog is , so the daily swim must be at least m. Solve to get . The combined daily distance first reaches m on day 37 (day 36 gives m).
Common mistakes
This asks for a daily threshold, not the day the cumulative distance passes 2.4 km.