Quick Concept Summary
This topic is a two-speed story: one speed belongs to the boat, the other to the stream. Downstream adds them; upstream subtracts them.
Worked Examples
Example 1: Find still-water speed
Downstream speed = 18 km/h, upstream speed = 10 km/h.
Boat speed = (18 + 10)/2 = 14 km/h
Stream speed = (18 - 10)/2 = 4 km/h
Example 2: Find time
A boat moves downstream at 20 km/h. How long to cover 60 km?
Time = 60/20 = 3 hours
Example 3: Build upstream/downstream speeds
Boat speed in still water = 12 km/h, stream speed = 3 km/h.
Downstream = 15 km/h
Upstream = 9 km/h
Practice Questions
1. Downstream = 24 km/h, upstream = 16 km/h. Find boat speed and stream speed. 2. A boat speed is 15 km/h and stream speed is 2 km/h. Find upstream speed. 3. A boat covers 42 km downstream in 3 hours. Find downstream speed. 4. A boat covers equal distances upstream and downstream. Why is average speed not the simple average? 5. A stream speed increases while boat speed stays same. What happens upstream?
Common Mistakes
- Reversing upstream and downstream
- Forgetting the half-sum and half-difference shortcuts
- Using simple average in equal-distance round trips
Revision Checklist
- [ ] Downstream and upstream formulas
- [ ] Half-sum / half-difference shortcuts
- [ ] Time-distance relation