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 travels 72 km upstream in 9 hours. If the stream's speed is 1 km/h, what is the boat's speed in still water?
Practice 2easy
A boat's speed in still water is 10 km/h and the stream's speed is 3 km/h. How long will it take the boat to travel 91 km upstream?
Practice 3easy
A boat takes 5 hours to travel 100 km downstream. If the boat's speed in still water is 18 km/h, what is the speed of the stream?
Practice 4easy
A boat's upstream speed is 12 km/h and its downstream speed is 18 km/h. What is the speed of the stream?
Practice 5easy
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 6easy
A boat covers 60 km downstream and 40 km upstream in the same time. If the stream's speed is 5 km/h, find the boat's speed in still water.
Practice 7medium
A boat's speed in still water is 12 km/h. It takes 2 hours to travel a certain distance downstream and 3 hours to travel the same distance upstream. What is the speed of the stream?
Practice 8medium
A swimmer swims 24 km downstream in 2 hours and 24 km upstream in 4 hours. If the swimmer swims at a constant speed in still water, what is the speed of the current?
Practice 9medium
The speed of a boat in still water is 15 km/h and the speed of the stream is 3 km/h. How long will it take the boat to travel 72 km downstream and then return to the starting point?
Practice 10medium
A boat can travel 20 km upstream in the same time it travels 30 km downstream. If the speed of the stream is 5 km/h, what is the speed of the boat in still water?
Practice 11hard
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, how long will it take him?
Practice 12hard
A boat travels 84 km downstream and returns upstream to the starting point. The downstream journey takes 4 hours and the upstream journey takes 7 hours. A swimmer with the same speed in still water as the boat takes 6 hours to swim 36 km in still water. What is the stream's speed?
Practice 13hard
A boat's speed in still water is 20 km/h. It travels 150 km downstream and then returns. If the total time taken is 16 hours, what is the speed of the stream? (Assume the boat travels at constant speed in still water throughout.)