Downstream & Upstream

🎯 Learning Objective

Set up downstream and upstream speeds and recover boat and stream speeds from them.

💡 Concept

• Boat speed in still water = b; stream speed = s
• Downstream (with the current): b + s | Upstream (against it): b − s
• b = (Downstream + Upstream)/2
• s = (Downstream − Upstream)/2
• Downstream is always the faster one — if not, you have swapped them

🧮 Key Formulas

Down = b + s

>

Up = b − s

>

b = (D + U)/2

>

s = (D − U)/2

✏️ Easy Example

Q. A boat's speed in still water is 10 km/h and the stream flows at 2 km/h. Find its downstream and upstream speeds.

1. Down = 10 + 2 = 12 km/h
2. Up = 10 − 2 = 8 km/h

Answer: 12 km/h and 8 km/h

🇮🇳 Real-Life Example

On the Ganga ghats of Varanasi the boatman quotes more for the return leg — rowing against the current is genuinely slower, and b − s is priced into the fare.

📝 Exam-Level Example

Q. A boat goes 24 km downstream in 2 hours and returns in 3 hours. Find the speed of the boat in still water and of the stream.

1. Down = 24/2 = 12 km/h; Up = 24/3 = 8 km/h
2. b = (12 + 8)/2 = 10
3. s = (12 − 8)/2 = 2

Answer: Boat 10 km/h, stream 2 km/h

📝 Exam-Level Example

Q. A man rows at 15 km/h in still water; the stream is 3 km/h. How long will he take to row 54 km downstream?

1. Down = 15 + 3 = 18 km/h
2. Time = 54 ÷ 18

Answer: 3 hours

🪄 Memory Trick

Given down and up speeds? Boat = their average, stream = half their gap. No equations needed.

⚠️ Common Mistakes

• ❌ Swapping downstream and upstream
• ❌ Dividing the gap by 2 and calling it the boat speed (that half-gap is the stream)

🏆 Exam Tips

• ✅ Still-water speed always lies between up and down speeds
• ✅ Distance and time given? Convert to speeds before anything else

📌 Summary

• Down = b + s, Up = b − s
• b = (D + U)/2
• s = (D − U)/2
• Downstream must be the bigger number