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. A boat’s speed in still water is 9 km/hr and the stream flows at 6 km/hr. A man rows to a certain place and back, taking a total of 1 hour 36 minutes. What is the one-way distance to that place?
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Answer: B
Let boat speed in still water = B = 9 km/hr and stream speed = S = 6 km/hr. Downstream speed = B + S = 9 + 6 = 15 km/hr. Upstream speed = B – S = 9 – 6 = 3 km/hr. Let d be the one-way distance in km. Time downstream = d/15 and time upstream = d/3. Total time: d/15 + d/3 = 1 hour 36 minutes. Solving this equation gives d = 4 km. Check: time downstream = 4/15 and time upstream = 4/3; these add up to 1 hour 36 minutes.
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Q2. A boat’s speed in still water is 7 km/hr and the stream flows at 5 km/hr. A man rows to a certain place and back, taking a total of 20 hours 25 minutes. What is the one-way distance to that place?
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Answer: D
Let boat speed in still water = B = 7 km/hr and stream speed = S = 5 km/hr. Downstream speed = B + S = 7 + 5 = 12 km/hr. Upstream speed = B – S = 7 – 5 = 2 km/hr. Let d be the one-way distance in km. Time downstream = d/12 and time upstream = d/2. Total time: d/12 + d/2 = 20 hours 25 minutes. Solving this equation gives d = 35 km. Check: time downstream = 35/12 and time upstream = 35/2; these add up to 20 hours 25 minutes.
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Q3. A boat’s speed in still water is 15 km/hr and the stream flows at 5 km/hr. A man rows to a certain place and back, taking a total of 2 hours 51 minutes. What is the one-way distance to that place?
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Answer: C
Let boat speed in still water = B = 15 km/hr and stream speed = S = 5 km/hr. Downstream speed = B + S = 15 + 5 = 20 km/hr. Upstream speed = B – S = 15 – 5 = 10 km/hr. Let d be the one-way distance in km. Time downstream = d/20 and time upstream = d/10. Total time: d/20 + d/10 = 2 hours 51 minutes. Solving this equation gives d = 19 km. Check: time downstream = 19/20 and time upstream = 19/10; these add up to 2 hours 51 minutes.
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Q4. A boat’s speed in still water is 5 km/hr and the stream flows at 3 km/hr. A man rows to a certain place and back, taking a total of 6 hours 15 minutes. What is the one-way distance to that place?
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Answer: A
Let boat speed in still water = B = 5 km/hr and stream speed = S = 3 km/hr. Downstream speed = B + S = 5 + 3 = 8 km/hr. Upstream speed = B – S = 5 – 3 = 2 km/hr. Let d be the one-way distance in km. Time downstream = d/8 and time upstream = d/2. Total time: d/8 + d/2 = 6 hours 15 minutes. Solving this equation gives d = 10 km. Check: time downstream = 10/8 and time upstream = 10/2; these add up to 6 hours 15 minutes.
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Q5. A boat’s speed in still water is 7 km/hr and the stream flows at 5 km/hr. A man rows to a certain place and back, taking a total of 14 hours 35 minutes. What is the one-way distance to that place?
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Answer: B
Let boat speed in still water = B = 7 km/hr and stream speed = S = 5 km/hr. Downstream speed = B + S = 7 + 5 = 12 km/hr. Upstream speed = B – S = 7 – 5 = 2 km/hr. Let d be the one-way distance in km. Time downstream = d/12 and time upstream = d/2. Total time: d/12 + d/2 = 14 hours 35 minutes. Solving this equation gives d = 25 km. Check: time downstream = 25/12 and time upstream = 25/2; these add up to 14 hours 35 minutes.
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Q6. Neha can row 16 km/hr in still water. It takes Neha 3 times as long to row upstream as to row downstream. Find the rate of the stream.
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Answer: C
Let boat speed in still water = B = 16 km/hr and stream speed = S. Downstream speed = B + S and upstream speed = B – S. For the same distance, upstream time is 3 times downstream time. Time and speed are inversely related for a fixed distance. So downstream speed must be 3 times upstream speed: B + S = 3 x (B – S). Expanding: B + S = 3B – 3S. Collecting S terms: S + 3S = 3B – B. So S x (3+1) = B x (3-1). S = B x (3-1)/(3+1) = 16 x (3-1)/(3+1) = 8 km/hr. Check: downstream speed = 24 km/hr, upstream speed = 8 km/hr, and 24/8 equals 3, as required.
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Q7. Sanjay can row 6 km/hr in still water. It takes Sanjay 3 times as long to row upstream as to row downstream. Find the rate of the stream.
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Answer: D
Let boat speed in still water = B = 6 km/hr and stream speed = S. Downstream speed = B + S and upstream speed = B – S. For the same distance, upstream time is 3 times downstream time. Time and speed are inversely related for a fixed distance. So downstream speed must be 3 times upstream speed: B + S = 3 x (B – S). Expanding: B + S = 3B – 3S. Collecting S terms: S + 3S = 3B – B. So S x (3+1) = B x (3-1). S = B x (3-1)/(3+1) = 6 x (3-1)/(3+1) = 3 km/hr. Check: downstream speed = 9 km/hr, upstream speed = 3 km/hr, and 9/3 equals 3, as required.
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Q8. Priya can row 15 km/hr in still water. It takes Priya twice as long to row upstream as to row downstream. Find the rate of the stream.
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Answer: B
Let boat speed in still water = B = 15 km/hr and stream speed = S. Downstream speed = B + S and upstream speed = B – S. For the same distance, upstream time is twice downstream time. Time and speed are inversely related for a fixed distance. So downstream speed must be twice upstream speed: B + S = 2 x (B – S). Expanding: B + S = 2B – 2S. Collecting S terms: S + 2S = 2B – B. So S x (2+1) = B x (2-1). S = B x (2-1)/(2+1) = 15 x (2-1)/(2+1) = 5 km/hr. Check: downstream speed = 20 km/hr, upstream speed = 10 km/hr, and 20/10 equals 2, as required.
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Q9. Meera can row 9 km/hr in still water. It takes Meera twice as long to row upstream as to row downstream. Find the rate of the stream.
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Answer: A
Let boat speed in still water = B = 9 km/hr and stream speed = S. Downstream speed = B + S and upstream speed = B – S. For the same distance, upstream time is twice downstream time. Time and speed are inversely related for a fixed distance. So downstream speed must be twice upstream speed: B + S = 2 x (B – S). Expanding: B + S = 2B – 2S. Collecting S terms: S + 2S = 2B – B. So S x (2+1) = B x (2-1). S = B x (2-1)/(2+1) = 9 x (2-1)/(2+1) = 3 km/hr. Check: downstream speed = 12 km/hr, upstream speed = 6 km/hr, and 12/6 equals 2, as required.
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Q10. Neha can row 15 km/hr in still water. It takes Neha twice as long to row upstream as to row downstream. Find the rate of the stream.
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Answer: D
Let boat speed in still water = B = 15 km/hr and stream speed = S. Downstream speed = B + S and upstream speed = B – S. For the same distance, upstream time is twice downstream time. Time and speed are inversely related for a fixed distance. So downstream speed must be twice upstream speed: B + S = 2 x (B – S). Expanding: B + S = 2B – 2S. Collecting S terms: S + 2S = 2B – B. So S x (2+1) = B x (2-1). S = B x (2-1)/(2+1) = 15 x (2-1)/(2+1) = 5 km/hr. Check: downstream speed = 20 km/hr, upstream speed = 10 km/hr, and 20/10 equals 2, as required.
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Q11. Neha can row 18 km/hr in still water. It takes Neha 3 times as long to row upstream as to row downstream. Find the rate of the stream.
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Answer: C
Let boat speed in still water = B = 18 km/hr and stream speed = S. Downstream speed = B + S and upstream speed = B – S. For the same distance, upstream time is 3 times downstream time. Time and speed are inversely related for a fixed distance. So downstream speed must be 3 times upstream speed: B + S = 3 x (B – S). Expanding: B + S = 3B – 3S. Collecting S terms: S + 3S = 3B – B. So S x (3+1) = B x (3-1). S = B x (3-1)/(3+1) = 18 x (3-1)/(3+1) = 9 km/hr. Check: downstream speed = 27 km/hr, upstream speed = 9 km/hr, and 27/9 equals 3, as required.
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Q12. Neha can row 10 km/hr in still water. It takes Neha 3/2 times as long to row upstream as to row downstream. Find the rate of the stream.
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Answer: B
Let boat speed in still water = B = 10 km/hr and stream speed = S. Downstream speed = B + S and upstream speed = B – S. For the same distance, upstream time is 3/2 times downstream time. Time and speed are inversely related for a fixed distance. So downstream speed must be 3/2 times upstream speed: B + S = 1.5 x (B – S). Expanding: B + S = 1.5B – 1.5S. Collecting S terms: S + 1.5S = 1.5B – B. So S x (1.5+1) = B x (1.5-1). S = B x (1.5-1)/(1.5+1) = 10 x (1.5-1)/(1.5+1) = 2 km/hr. Check: downstream speed = 12 km/hr, upstream speed = 8 km/hr, and 12/8 equals 1.5, as required.
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Q13. Karan can row 14 km/hr in still water. It takes Karan 3 times as long to row upstream as to row downstream. Find the rate of the stream.
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Answer: A
Let boat speed in still water = B = 14 km/hr and stream speed = S. Downstream speed = B + S and upstream speed = B – S. For the same distance, upstream time is 3 times downstream time. Time and speed are inversely related for a fixed distance. So downstream speed must be 3 times upstream speed: B + S = 3 x (B – S). Expanding: B + S = 3B – 3S. Collecting S terms: S + 3S = 3B – B. So S x (3+1) = B x (3-1). S = B x (3-1)/(3+1) = 14 x (3-1)/(3+1) = 7 km/hr. Check: downstream speed = 21 km/hr, upstream speed = 7 km/hr, and 21/7 equals 3, as required.
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Q14. Karan can row 18 km/hr in still water. It takes Karan 3 times as long to row upstream as to row downstream. Find the rate of the stream.
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Answer: C
Let boat speed in still water = B = 18 km/hr and stream speed = S. Downstream speed = B + S and upstream speed = B – S. For the same distance, upstream time is 3 times downstream time. Time and speed are inversely related for a fixed distance. So downstream speed must be 3 times upstream speed: B + S = 3 x (B – S). Expanding: B + S = 3B – 3S. Collecting S terms: S + 3S = 3B – B. So S x (3+1) = B x (3-1). S = B x (3-1)/(3+1) = 18 x (3-1)/(3+1) = 9 km/hr. Check: downstream speed = 27 km/hr, upstream speed = 9 km/hr, and 27/9 equals 3, as required.
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Q15. Divya can row 8 km/hr in still water. It takes Divya 3 times as long to row upstream as to row downstream. Find the rate of the stream.
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Answer: D
Let boat speed in still water = B = 8 km/hr and stream speed = S. Downstream speed = B + S and upstream speed = B – S. For the same distance, upstream time is 3 times downstream time. Time and speed are inversely related for a fixed distance. So downstream speed must be 3 times upstream speed: B + S = 3 x (B – S). Expanding: B + S = 3B – 3S. Collecting S terms: S + 3S = 3B – B. So S x (3+1) = B x (3-1). S = B x (3-1)/(3+1) = 8 x (3-1)/(3+1) = 4 km/hr. Check: downstream speed = 12 km/hr, upstream speed = 4 km/hr, and 12/4 equals 3, as required.
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Q16. The speed of a motorboat in still water is to the speed of the current as 8 : 1. The boat goes downstream in 7 hours. How long will it take to come back upstream?
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Answer: A
Let boat speed in still water = 8 units and stream speed = 1 units. Downstream speed = 8 + 1 = 9 units. Upstream speed = 8 – 1 = 7 units. The distance is the same both ways. Distance = downstream speed x downstream time = 9 x 7 = 63 unit-hours. Time upstream = distance / upstream speed = 63 / 7 = 9. So the time upstream is 9 hours. Check: 7 x 9 = 63, which matches the distance of 63 unit-hours.
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Q17. The speed of a motorboat in still water is to the speed of the current as 7 : 4. The boat goes downstream in 6 hours. How long will it take to come back upstream?
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Answer: D
Let boat speed in still water = 7 units and stream speed = 4 units. Downstream speed = 7 + 4 = 11 units. Upstream speed = 7 – 4 = 3 units. The distance is the same both ways. Distance = downstream speed x downstream time = 11 x 6 = 66 unit-hours. Time upstream = distance / upstream speed = 66 / 3 = 22. So the time upstream is 22 hours. Check: 3 x 22 = 66, which matches the distance of 66 unit-hours.
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Q18. The speed of a motorboat in still water is to the speed of the current as 12 : 5. The boat goes downstream in 7 hours. How long will it take to come back upstream?
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Answer: B
Let boat speed in still water = 12 units and stream speed = 5 units. Downstream speed = 12 + 5 = 17 units. Upstream speed = 12 – 5 = 7 units. The distance is the same both ways. Distance = downstream speed x downstream time = 17 x 7 = 119 unit-hours. Time upstream = distance / upstream speed = 119 / 7 = 17. So the time upstream is 17 hours. Check: 7 x 17 = 119, which matches the distance of 119 unit-hours.
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Q19. The speed of a motorboat in still water is to the speed of the current as 5 : 3. The boat goes downstream in 7 hours. How long will it take to come back upstream?
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Answer: C
Let boat speed in still water = 5 units and stream speed = 3 units. Downstream speed = 5 + 3 = 8 units. Upstream speed = 5 – 3 = 2 units. The distance is the same both ways. Distance = downstream speed x downstream time = 8 x 7 = 56 unit-hours. Time upstream = distance / upstream speed = 56 / 2 = 28. So the time upstream is 28 hours. Check: 2 x 28 = 56, which matches the distance of 56 unit-hours.
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Q20. The speed of a motorboat in still water is to the speed of the current as 11 : 8. The boat goes downstream in 3 hours. How long will it take to come back upstream?
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Answer: A
Let boat speed in still water = 11 units and stream speed = 8 units. Downstream speed = 11 + 8 = 19 units. Upstream speed = 11 – 8 = 3 units. The distance is the same both ways. Distance = downstream speed x downstream time = 19 x 3 = 57 unit-hours. Time upstream = distance / upstream speed = 57 / 3 = 19. So the time upstream is 19 hours. Check: 3 x 19 = 57, which matches the distance of 57 unit-hours.
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Q21. The speed of a motorboat in still water is to the speed of the current as 11 : 9. The boat goes downstream in 3 hours. How long will it take to come back upstream?
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Answer: B
Let boat speed in still water = 11 units and stream speed = 9 units. Downstream speed = 11 + 9 = 20 units. Upstream speed = 11 – 9 = 2 units. The distance is the same both ways. Distance = downstream speed x downstream time = 20 x 3 = 60 unit-hours. Time upstream = distance / upstream speed = 60 / 2 = 30. So the time upstream is 30 hours. Check: 2 x 30 = 60, which matches the distance of 60 unit-hours.
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Q22. The speed of a motorboat in still water is to the speed of the current as 7 : 5. The boat goes downstream in 2 hours. How long will it take to come back upstream?
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Answer: C
Let boat speed in still water = 7 units and stream speed = 5 units. Downstream speed = 7 + 5 = 12 units. Upstream speed = 7 – 5 = 2 units. The distance is the same both ways. Distance = downstream speed x downstream time = 12 x 2 = 24 unit-hours. Time upstream = distance / upstream speed = 24 / 2 = 12. So the time upstream is 12 hours. Check: 2 x 12 = 24, which matches the distance of 24 unit-hours.
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Q23. The speed of a motorboat in still water is to the speed of the current as 7 : 3. The boat goes downstream in 2 hours. How long will it take to come back upstream?
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Answer: D
Let boat speed in still water = 7 units and stream speed = 3 units. Downstream speed = 7 + 3 = 10 units. Upstream speed = 7 – 3 = 4 units. The distance is the same both ways. Distance = downstream speed x downstream time = 10 x 2 = 20 unit-hours. Time upstream = distance / upstream speed = 20 / 4 = 5. So the time upstream is 5 hours. Check: 4 x 5 = 20, which matches the distance of 20 unit-hours.
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Q24. The speed of a motorboat in still water is to the speed of the current as 9 : 2. The boat goes downstream in 7 hours. How long will it take to come back upstream?
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Answer: D
Let boat speed in still water = 9 units and stream speed = 2 units. Downstream speed = 9 + 2 = 11 units. Upstream speed = 9 – 2 = 7 units. The distance is the same both ways. Distance = downstream speed x downstream time = 11 x 7 = 77 unit-hours. Time upstream = distance / upstream speed = 77 / 7 = 11. So the time upstream is 11 hours. Check: 7 x 11 = 77, which matches the distance of 77 unit-hours.
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Q25. The speed of a motorboat in still water is to the speed of the current as 5 : 3. The boat goes downstream in 10 hours. How long will it take to come back upstream?
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Answer: C
Let boat speed in still water = 5 units and stream speed = 3 units. Downstream speed = 5 + 3 = 8 units. Upstream speed = 5 – 3 = 2 units. The distance is the same both ways. Distance = downstream speed x downstream time = 8 x 10 = 80 unit-hours. Time upstream = distance / upstream speed = 80 / 2 = 40. So the time upstream is 40 hours. Check: 2 x 40 = 80, which matches the distance of 80 unit-hours.
Related topics: Boats and Streams: Formulas, Shortcuts and Solved Examples