The Rongai route has several variations. It can be done as a five, six or even seven day trek.
The extra day is not spent in the same camp as the previous day (on the Marangu route it is). The six day trek usually follows a different trail after day two. Some operators of six day treks simply ascend slower, making an extra camp instead of the detour. All seven day treks make the detour.
This itinerary describes the six day trek with the detour via Mawenzi Tarn hut, one of the most scenic campsites on the mountain.
(Note: altitudes and distances are approximations. Different sources will give you different numbers.)

Starts from Arusha

Duration: 6 days

Day 1 – Nalemoru (1950 m/6400 ft) – First Cave Campsite (2650 m/8700 ft)
Walking distance: 6.5 km/4 miles
Walking time: 3-4 hours
Altitude gain: 700 m/2300 ft

Day 2 – First Cave Campsite – Kikelewa Caves (3600 m/11810 ft)
Walking distance: 9 km/5.6 miles
Walking time: 6-7 hours
Altitude gain: 950 m/3110 ft

Day 3 – Kikelewa Caves – Mawenzi Tarn (4330 m/14210 ft)
Walking distance: 6 km/3.7 miles
Walking time: 3-4 hours
Altitude gain: 730 m/2400 ft
Afternoon acclimatization walk to about 4500 m/14760 ft

Day 4 – Mawenzi Tarn – Kibo Huts (4700 m/15420 ft)
Walking distance: 9 km/5.6 miles
Walking time: 4-5 hours
Altitude gain: 370 m/1215 ft

Day 5 – Summit attempt via Gilman’s Point (5700 m/18700 ft) to Uhuru Peak (5895 m/19340 ft) and descent to Horombo Huts (3700 m/12200 ft)
Walking distance: 5 km/3.1 miles ascent + 15 km/9.3 miles descent
Walking time: 5-6 hrs + 1-2 hours up, 5-6 hours down (the overall walking time may vary from 10 – 16 hours)
Altitude gain: 1000 m/ 3280 ft (Gilman’s Point) or 1195 m/3920 ft (Uhuru Peak)
Descent: 2195 m/7200 ft

Day 5 – Horombo Huts – Marangu Gate
Walking distance: 20 km/12.5 miles
Walking time: 5 hours
Descent: 1840 m/6040 ft
Transfer back to Arusha.