Boats & Streams • Topic 1 of 3

Upstream & Downstream

Fix the two definitions and the topic opens up. Downstream means moving in the direction of the current, so the river pushes the boat and the effective speed is b + s. Upstream means moving against the current, so the river drags and the speed is b − s. Here b is the boat’s still-water speed and s the stream speed, with b > s always (else the boat cannot go upstream). Almost every elementary question is just Time = Distance ÷ (effective speed). The single most useful habit in CAT is to keep speeds in km/h and convert any "metres in seconds" data using 1 m/s = 18/5 km/h before plugging in. When a problem mixes a man rowing and a current, treat "rowing speed in still water" as b and "speed of current" as s — the words change but the algebra does not.

✅ Solved examples

1. A boat’s still-water speed is 12 km/h and the stream flows at 3 km/h. Find its downstream and upstream speeds.
Downstream = b + s = 12 + 3 = 15 km/h. Upstream = b − s = 12 − 3 = 9 km/h.
2. A boat covers 45 km downstream in 3 hours. If the stream is 4 km/h, find the still-water speed.
Downstream speed = 45/3 = 15 km/h = b + s ⇒ b = 15 − 4 = 11 km/h.
3. A man rows at 9 km/h in still water against a current of 2 km/h. How long to cover 21 km upstream?
Upstream speed = 9 − 2 = 7 km/h. Time = 21/7 = 3 hours.
4. A boat goes 30 km downstream in 2 hours and the same 30 km upstream in 3 hours. Find b and s.
D = 30/2 = 15, U = 30/3 = 10. b = (15+10)/2 = 12.5 km/h, s = (15−10)/2 = 2.5 km/h.

✏️ Practice — try these, take hints as needed

1. Boat speed 10 km/h, stream 2 km/h. Find downstream and upstream speeds.
Downstream adds, upstream subtracts.
b + s and b − s.
10 ± 2.
Downstream 12 km/h, upstream 8 km/h
2. A boat covers 36 km upstream in 4 hours; stream is 1 km/h. Find still-water speed.
Upstream speed = 36/4.
That equals b − s.
9 = b − 1.
10 km/h
3. Still-water speed 15 km/h, current 5 km/h. Time to row 40 km downstream?
Downstream speed = 15 + 5.
= 20 km/h.
40 ÷ 20.
2 hours
4. A boat does 24 km downstream in 2 h and 24 km upstream in 3 h. Find the stream speed.
D = 12, U = 8.
s = (D − U)/2.
(12 − 8)/2.
2 km/h
5. A swimmer’s still-water speed is 5 km/h, current 1 km/h. He swims 12 km against the current. Time taken?
Upstream = 5 − 1.
= 4 km/h.
12 ÷ 4.
3 hours

📝 Topic test — 8 questions

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