Boats and streams questions ask how fast a boat moves with and against the flow of a river. The maths is simple once you picture the arrows.
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Q1. The speed of a motorboat in still water is to the speed of the current as 4 : 1. The boat goes downstream in 6 hours. How long will it take to come back upstream?
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Answer: B
Let boat speed in still water = 4 units and stream speed = 1 units. Downstream speed = 4 + 1 = 5 units. Upstream speed = 4 – 1 = 3 units. The distance is the same both ways. Distance = downstream speed x downstream time = 5 x 6 = 30 unit-hours. Time upstream = distance / upstream speed = 30 / 3 = 10. So the time upstream is 10 hours. Check: 3 x 10 = 30, which matches the distance of 30 unit-hours.
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Q2. The speed of a motorboat in still water is to the speed of the current as 5 : 1. The boat goes downstream in 2 hours. How long will it take to come back upstream?
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Answer: A
Let boat speed in still water = 5 units and stream speed = 1 units. Downstream speed = 5 + 1 = 6 units. Upstream speed = 5 – 1 = 4 units. The distance is the same both ways. Distance = downstream speed x downstream time = 6 x 2 = 12 unit-hours. Time upstream = distance / upstream speed = 12 / 4 = 3. So the time upstream is 3 hours. Check: 4 x 3 = 12, which matches the distance of 12 unit-hours.
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Q3. Rohan rows a boat whose speed in still water is 16 km/hr, in a stream flowing at 9 km/hr. How long will Rohan take to row 25 km downstream?
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Answer: D
Let boat speed in still water = B = 16 km/hr and stream speed = S = 9 km/hr. Moving downstream, the current adds to the boat’s speed. So speed downstream = 16 + 9 = 25 km/hr. Time = distance / speed = 25 / 25 = 1. So the time taken is 1 hour. Check: speed x time = 25 x 1 = 25 km, matching the given distance of 25 km.
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Q4. Neha rows a boat whose speed in still water is 10 km/hr, in a stream flowing at 6 km/hr. How long will Neha take to row 32 km downstream?
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Answer: A
Let boat speed in still water = B = 10 km/hr and stream speed = S = 6 km/hr. Moving downstream, the current adds to the boat’s speed. So speed downstream = 10 + 6 = 16 km/hr. Time = distance / speed = 32 / 16 = 2. So the time taken is 2 hours. Check: speed x time = 16 x 2 = 32 km, matching the given distance of 32 km.
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Q5. Meera rows a boat whose speed in still water is 9 km/hr, in a stream flowing at 4 km/hr. How long will Meera take to row 5 km upstream?
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Answer: B
Let boat speed in still water = B = 9 km/hr and stream speed = S = 4 km/hr. Moving upstream, the current works against the boat’s speed. So speed upstream = 9 – 4 = 5 km/hr. Time = distance / speed = 5 / 5 = 1. So the time taken is 1 hour. Check: speed x time = 5 x 1 = 5 km, matching the given distance of 5 km.
Related topics: Boats and Streams: Formulas, Shortcuts and Solved Examples
Q6. Neha rows a boat whose speed in still water is 6 km/hr, in a stream flowing at 3 km/hr. How long will Neha take to row 18 km upstream?
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Answer: C
Let boat speed in still water = B = 6 km/hr and stream speed = S = 3 km/hr. Moving upstream, the current works against the boat’s speed. So speed upstream = 6 – 3 = 3 km/hr. Time = distance / speed = 18 / 3 = 6. So the time taken is 6 hours. Check: speed x time = 3 x 6 = 18 km, matching the given distance of 18 km.
Related topics: Boats and Streams: Formulas, Shortcuts and Solved Examples
Q7. Sanjay rows a boat whose speed in still water is 13 km/hr, in a stream flowing at 11 km/hr. How long will Sanjay take to row 24 km downstream?
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Answer: C
Let boat speed in still water = B = 13 km/hr and stream speed = S = 11 km/hr. Moving downstream, the current adds to the boat’s speed. So speed downstream = 13 + 11 = 24 km/hr. Time = distance / speed = 24 / 24 = 1. So the time taken is 1 hour. Check: speed x time = 24 x 1 = 24 km, matching the given distance of 24 km.
Related topics: Boats and Streams: Formulas, Shortcuts and Solved Examples
Q8. Rohan rows a boat whose speed in still water is 14 km/hr, in a stream flowing at 4 km/hr. How long will Rohan take to row 54 km downstream?
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Answer: D
Let boat speed in still water = B = 14 km/hr and stream speed = S = 4 km/hr. Moving downstream, the current adds to the boat’s speed. So speed downstream = 14 + 4 = 18 km/hr. Time = distance / speed = 54 / 18 = 3. So the time taken is 3 hours. Check: speed x time = 18 x 3 = 54 km, matching the given distance of 54 km.
Related topics: Boats and Streams: Formulas, Shortcuts and Solved Examples
Q9. Arjun rows a boat whose speed in still water is 10 km/hr, in a stream flowing at 4 km/hr. How long will Arjun take to row 12 km upstream?
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Answer: B
Let boat speed in still water = B = 10 km/hr and stream speed = S = 4 km/hr. Moving upstream, the current works against the boat’s speed. So speed upstream = 10 – 4 = 6 km/hr. Time = distance / speed = 12 / 6 = 2. So the time taken is 2 hours. Check: speed x time = 6 x 2 = 12 km, matching the given distance of 12 km.
Related topics: Boats and Streams: Formulas, Shortcuts and Solved Examples
Q10. Vikram rows a boat whose speed in still water is 9 km/hr, in a stream flowing at 5 km/hr. How long will Vikram take to row 14 km downstream?
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Answer: A
Let boat speed in still water = B = 9 km/hr and stream speed = S = 5 km/hr. Moving downstream, the current adds to the boat’s speed. So speed downstream = 9 + 5 = 14 km/hr. Time = distance / speed = 14 / 14 = 1. So the time taken is 1 hour. Check: speed x time = 14 x 1 = 14 km, matching the given distance of 14 km.
Related topics: Boats and Streams: Formulas, Shortcuts and Solved Examples
Q11. Vikram rows a boat whose speed in still water is 6 km/hr, in a stream flowing at 3 km/hr. How long will Vikram take to row 12 km upstream?
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Answer: D
Let boat speed in still water = B = 6 km/hr and stream speed = S = 3 km/hr. Moving upstream, the current works against the boat’s speed. So speed upstream = 6 – 3 = 3 km/hr. Time = distance / speed = 12 / 3 = 4. So the time taken is 4 hours. Check: speed x time = 3 x 4 = 12 km, matching the given distance of 12 km.
Related topics: Boats and Streams: Formulas, Shortcuts and Solved Examples
Q12. Vikram rows a boat whose speed in still water is 7 km/hr, in a stream flowing at 2 km/hr. How long will Vikram take to row 15 km upstream?
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Answer: A
Let boat speed in still water = B = 7 km/hr and stream speed = S = 2 km/hr. Moving upstream, the current works against the boat’s speed. So speed upstream = 7 – 2 = 5 km/hr. Time = distance / speed = 15 / 5 = 3. So the time taken is 3 hours. Check: speed x time = 5 x 3 = 15 km, matching the given distance of 15 km.
Related topics: Boats and Streams: Formulas, Shortcuts and Solved Examples
Q13. Divya rows a boat whose speed in still water is 9 km/hr, in a stream flowing at 5 km/hr. How long will Divya take to row 70 km downstream?
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Answer: C
Let boat speed in still water = B = 9 km/hr and stream speed = S = 5 km/hr. Moving downstream, the current adds to the boat’s speed. So speed downstream = 9 + 5 = 14 km/hr. Time = distance / speed = 70 / 14 = 5. So the time taken is 5 hours. Check: speed x time = 14 x 5 = 70 km, matching the given distance of 70 km.
Related topics: Boats and Streams: Formulas, Shortcuts and Solved Examples
Q14. Priya rows a boat whose speed in still water is 12 km/hr, in a stream flowing at 10 km/hr. How long will Priya take to row 10 km upstream?
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Answer: B
Let boat speed in still water = B = 12 km/hr and stream speed = S = 10 km/hr. Moving upstream, the current works against the boat’s speed. So speed upstream = 12 – 10 = 2 km/hr. Time = distance / speed = 10 / 2 = 5. So the time taken is 5 hours. Check: speed x time = 2 x 5 = 10 km, matching the given distance of 10 km.
Related topics: Boats and Streams: Formulas, Shortcuts and Solved Examples
Q15. Karan rows a boat whose speed in still water is 10 km/hr, in a stream flowing at 6 km/hr. How long will Karan take to row 32 km downstream?
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Answer: C
Let boat speed in still water = B = 10 km/hr and stream speed = S = 6 km/hr. Moving downstream, the current adds to the boat’s speed. So speed downstream = 10 + 6 = 16 km/hr. Time = distance / speed = 32 / 16 = 2. So the time taken is 2 hours. Check: speed x time = 16 x 2 = 32 km, matching the given distance of 32 km.
Related topics: Boats and Streams: Formulas, Shortcuts and Solved Examples
Q16. Priya rows a boat whose speed in still water is 17 km/hr, in a stream flowing at 7 km/hr. How long will Priya take to row 60 km upstream?
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Answer: D
Let boat speed in still water = B = 17 km/hr and stream speed = S = 7 km/hr. Moving upstream, the current works against the boat’s speed. So speed upstream = 17 – 7 = 10 km/hr. Time = distance / speed = 60 / 10 = 6. So the time taken is 6 hours. Check: speed x time = 10 x 6 = 60 km, matching the given distance of 60 km.
Related topics: Boats and Streams: Formulas, Shortcuts and Solved Examples
Q17. A boat travels downstream at 14 km/hr and upstream at 4 km/hr. What is the speed of the stream?
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Answer: B
Let downstream speed = 14 km/hr and upstream speed = 4 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Subtracting the upstream equation from the downstream one cancels B: (B+S) – (B-S) = 2S. So 14 – 4 = 2S, which gives 2S = 10. S = 10/2 = 5 km/hr. Check: 4 (upstream) + 10 (twice the stream speed) = 14, matching the downstream speed 14.
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Q18. A boat travels downstream at 15 km/hr and upstream at 3 km/hr. What is the speed of the stream?
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Answer: A
Let downstream speed = 15 km/hr and upstream speed = 3 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Subtracting the upstream equation from the downstream one cancels B: (B+S) – (B-S) = 2S. So 15 – 3 = 2S, which gives 2S = 12. S = 12/2 = 6 km/hr. Check: 3 (upstream) + 12 (twice the stream speed) = 15, matching the downstream speed 15.
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Q19. A boat travels downstream at 37 km/hr and upstream at 17 km/hr. What is the speed of the stream?
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Answer: C
Let downstream speed = 37 km/hr and upstream speed = 17 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Subtracting the upstream equation from the downstream one cancels B: (B+S) – (B-S) = 2S. So 37 – 17 = 2S, which gives 2S = 20. S = 20/2 = 10 km/hr. Check: 17 (upstream) + 20 (twice the stream speed) = 37, matching the downstream speed 37.
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Q20. A boat travels downstream at 17 km/hr and upstream at 13 km/hr. What is the speed of the stream?
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Answer: D
Let downstream speed = 17 km/hr and upstream speed = 13 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Subtracting the upstream equation from the downstream one cancels B: (B+S) – (B-S) = 2S. So 17 – 13 = 2S, which gives 2S = 4. S = 4/2 = 2 km/hr. Check: 13 (upstream) + 4 (twice the stream speed) = 17, matching the downstream speed 17.
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Q21. A boat travels downstream at 32 km/hr and upstream at 6 km/hr. What is the speed of the stream?
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Answer: A
Let downstream speed = 32 km/hr and upstream speed = 6 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Subtracting the upstream equation from the downstream one cancels B: (B+S) – (B-S) = 2S. So 32 – 6 = 2S, which gives 2S = 26. S = 26/2 = 13 km/hr. Check: 6 (upstream) + 26 (twice the stream speed) = 32, matching the downstream speed 32.
Related topics: Boats and Streams: Formulas, Shortcuts and Solved Examples
Q22. A boat travels downstream at 37 km/hr and upstream at 5 km/hr. What is the speed of the stream?
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Answer: B
Let downstream speed = 37 km/hr and upstream speed = 5 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Subtracting the upstream equation from the downstream one cancels B: (B+S) – (B-S) = 2S. So 37 – 5 = 2S, which gives 2S = 32. S = 32/2 = 16 km/hr. Check: 5 (upstream) + 32 (twice the stream speed) = 37, matching the downstream speed 37.
Related topics: Boats and Streams: Formulas, Shortcuts and Solved Examples
Q23. A boat travels downstream at 19 km/hr and upstream at 5 km/hr. What is the speed of the stream?
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Answer: B
Let downstream speed = 19 km/hr and upstream speed = 5 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Subtracting the upstream equation from the downstream one cancels B: (B+S) – (B-S) = 2S. So 19 – 5 = 2S, which gives 2S = 14. S = 14/2 = 7 km/hr. Check: 5 (upstream) + 14 (twice the stream speed) = 19, matching the downstream speed 19.
Related topics: Boats and Streams: Formulas, Shortcuts and Solved Examples
Q24. A boat travels downstream at 21 km/hr and upstream at 5 km/hr. What is the speed of the stream?
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Answer: D
Let downstream speed = 21 km/hr and upstream speed = 5 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Subtracting the upstream equation from the downstream one cancels B: (B+S) – (B-S) = 2S. So 21 – 5 = 2S, which gives 2S = 16. S = 16/2 = 8 km/hr. Check: 5 (upstream) + 16 (twice the stream speed) = 21, matching the downstream speed 21.
Related topics: Boats and Streams: Formulas, Shortcuts and Solved Examples
Q25. A boat travels downstream at 34 km/hr and upstream at 2 km/hr. What is the speed of the stream?
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Answer: A
Let downstream speed = 34 km/hr and upstream speed = 2 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Subtracting the upstream equation from the downstream one cancels B: (B+S) – (B-S) = 2S. So 34 – 2 = 2S, which gives 2S = 32. S = 32/2 = 16 km/hr. Check: 2 (upstream) + 32 (twice the stream speed) = 34, matching the downstream speed 34.
Related topics: Boats and Streams: Formulas, Shortcuts and Solved Examples