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 $200$ m and swims $200$ m. From day 2, jogging rises by $20\%$ of the previous day’s distance but is capped at $400$ m per day; swimming increases by $50$ m each day. Find the combined distance after 20 days, and the first day his combined daily distance reaches $2.4$ km.