Imagine walking on a moving escalator. If you walk in the same direction as the escalator, you move faster. If you walk against it, you move slower. Similarly, water current helps or hinders boat movement
💡Key Rules
Speed of boat in still water = (Downstream speed + Upstream speed) ÷ 2. Speed of current = (Downstream speed - Upstream speed) ÷ 2. Downstream speed = Boat speed + Stream speed. Upstream speed = Boat speed - Stream speed.
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Formula Block
Memorise — at least one formula appears in every paper
• Downstream Speed = Speed in still water + Speed of stream
• Upstream Speed = Speed in still water - Speed of stream
• Speed in still water = (Downstream + Upstream) ÷ 2
• Speed of stream = (Downstream - Upstream) ÷ 2
• Time = Distance ÷ Speed
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Exam Patterns
What examiners ask — read before attempting PYQs
Questions typically ask for boat speed in still water, stream speed, time calculations, or distance problems. Common formats include round trips, meeting point problems, and comparative speed questions.
Apply formulas
Boat speed in still water = (10 + 4) ÷ 2 = 7 km/hr
Stream speed = (10 - 4) ÷ 2 = 3 km/hr
Worked Example 2: A man can row 6 km/hr in still water. Stream speed is 2 km/hr. How long to travel 16 km downstream and return?
Calculate times
Time downstream = 16 ÷ 8 = 2 hours
Time upstream = 16 ÷ 4 = 4 hours
Total time = 2 + 4 = 6 hours
Trick for Round Trips: Total time = Distance × 2 × Boat speed ÷ (Boat speed² - Stream speed²)
Common Mistake: Students often confuse downstream and upstream directions
💡Remember
downstream means 'with the flow' (faster), upstream means 'against the flow' (slower). Another trap is adding stream speed when calculating upstream speed instead of subtracting it. Always check if your downstream speed is greater than upstream speed.
A boat covers 24 km upstream and 24 km downstream in a total of 10 hours. If the boat's speed in still water is 5 km/h, what is the speed of the stream?
Practice 2easy
A boatman rows 30 km downstream in 2 hours and the same distance upstream in 6 hours. What is the speed of the boat in still water?
Practice 3easy
A boat travels 48 km downstream in 3 hours. If the speed of the stream is 2 km/h, what is the speed of the boat in still water?
Practice 4easy
A boat's speed in still water is 10 km/h and the stream speed is 3 km/h. How long will it take the boat to travel 91 km upstream?
Practice 5easy
A man can row 36 km downstream in 4 hours and 32 km upstream in 8 hours. What is the speed of the stream?
Practice 6medium
The speed of a boat in still water is 15 km/h and the speed of the stream is 3 km/h. How much time will the boat take to cover 72 km downstream and then return to the starting point?
Practice 7medium
A boat can travel 20 km upstream in the same time it takes to travel 30 km downstream. If the speed of the stream is 5 km/h, what is the speed of the boat in still water?
Practice 8medium
A man rows a boat at a speed of 10 km/h in still water. The river flows at 2 km/h. If he rows 36 km downstream and then 36 km upstream, what is the average speed for the entire journey?
Practice 9medium
A swimmer swims 24 km downstream in 2 hours and 24 km upstream in 4 hours. What is the speed of the current?
Practice 10hard
Two boats, A and B, start from the same point. Boat A travels downstream at a speed of 18 km/h (in still water speed 15 km/h), while Boat B travels upstream at a speed of 10 km/h (in still water speed 13 km/h). After 2 hours, Boat A turns around and travels upstream, while Boat B turns around and travels downstream. How much time will it take for them to meet after they turn around?
Practice 11hard
A boat travels from Point P to Point Q (downstream) in 6 hours and returns from Q to P (upstream) in 9 hours. If the boat's speed in still water is 20 km/h, what is the distance between P and Q?
Practice 12hard
A boat travels 48 km downstream in 3 hours and 48 km upstream in 6 hours. A man swims at a constant speed in still water. If the man swims the same 48 km downstream, what time will he take if his swimming speed is half that of the boat's speed in still water?