Boats and Streams: Formulas, Shortcuts and Solved Examples — MCQs with Answers (Set 4)

Let downstream speed = 30 km/hr and upstream speed = 14 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 30 – 14 = 2S, which gives 2S = 16. S = 16/2 = 8 km/hr. Check: 14 (upstream) + 16 (twice the stream speed) = 30, matching the downstream speed 30.

Let downstream speed = 29 km/hr and upstream speed = 25 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 29 – 25 = 2S, which gives 2S = 4. S = 4/2 = 2 km/hr. Check: 25 (upstream) + 4 (twice the stream speed) = 29, matching the downstream speed 29.

Let downstream speed = 25 km/hr and upstream speed = 21 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 25 – 21 = 2S, which gives 2S = 4. S = 4/2 = 2 km/hr. Check: 21 (upstream) + 4 (twice the stream speed) = 25, matching the downstream speed 25.

Let downstream speed = 24 km/hr and upstream speed = 22 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Adding these two equations cancels S: (B+S) + (B-S) = 2B. So 24 + 22 = 2B, which gives 2B = 46. B = 46/2 = 23 km/hr. Check: this places B exactly halfway between the downstream speed 24 and the upstream speed 22.

Let downstream speed = 18 km/hr and upstream speed = 8 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Adding these two equations cancels S: (B+S) + (B-S) = 2B. So 18 + 8 = 2B, which gives 2B = 26. B = 26/2 = 13 km/hr. Check: this places B exactly halfway between the downstream speed 18 and the upstream speed 8.

Let downstream speed = 9 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. Adding these two equations cancels S: (B+S) + (B-S) = 2B. So 9 + 3 = 2B, which gives 2B = 12. B = 12/2 = 6 km/hr. Check: this places B exactly halfway between the downstream speed 9 and the upstream speed 3.

Let downstream speed = 37 km/hr and upstream speed = 29 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Adding these two equations cancels S: (B+S) + (B-S) = 2B. So 37 + 29 = 2B, which gives 2B = 66. B = 66/2 = 33 km/hr. Check: this places B exactly halfway between the downstream speed 37 and the upstream speed 29.

Let downstream speed = 38 km/hr and upstream speed = 36 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Adding these two equations cancels S: (B+S) + (B-S) = 2B. So 38 + 36 = 2B, which gives 2B = 74. B = 74/2 = 37 km/hr. Check: this places B exactly halfway between the downstream speed 38 and the upstream speed 36.

Let downstream speed = 40 km/hr and upstream speed = 16 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Adding these two equations cancels S: (B+S) + (B-S) = 2B. So 40 + 16 = 2B, which gives 2B = 56. B = 56/2 = 28 km/hr. Check: this places B exactly halfway between the downstream speed 40 and the upstream speed 16.

Let downstream speed = 37 km/hr and upstream speed = 33 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Adding these two equations cancels S: (B+S) + (B-S) = 2B. So 37 + 33 = 2B, which gives 2B = 70. B = 70/2 = 35 km/hr. Check: this places B exactly halfway between the downstream speed 37 and the upstream speed 33.

Let downstream speed = 34 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. Adding these two equations cancels S: (B+S) + (B-S) = 2B. So 34 + 4 = 2B, which gives 2B = 38. B = 38/2 = 19 km/hr. Check: this places B exactly halfway between the downstream speed 34 and the upstream speed 4.

Let downstream speed = 20 km/hr and upstream speed = 10 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Adding these two equations cancels S: (B+S) + (B-S) = 2B. So 20 + 10 = 2B, which gives 2B = 30. B = 30/2 = 15 km/hr. Check: this places B exactly halfway between the downstream speed 20 and the upstream speed 10.

Let downstream speed = 17 km/hr and upstream speed = 11 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Adding these two equations cancels S: (B+S) + (B-S) = 2B. So 17 + 11 = 2B, which gives 2B = 28. B = 28/2 = 14 km/hr. Check: this places B exactly halfway between the downstream speed 17 and the upstream speed 11.

Let downstream speed = 16 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. Adding these two equations cancels S: (B+S) + (B-S) = 2B. So 16 + 6 = 2B, which gives 2B = 22. B = 22/2 = 11 km/hr. Check: this places B exactly halfway between the downstream speed 16 and the upstream speed 6.

Let downstream speed = 16 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. Adding these two equations cancels S: (B+S) + (B-S) = 2B. So 16 + 2 = 2B, which gives 2B = 18. B = 18/2 = 9 km/hr. Check: this places B exactly halfway between the downstream speed 16 and the upstream speed 2.

Let boat speed in still water = B = 7 km/hr. Let stream speed = S = 3 km/hr. Downstream speed = B + S, because the current pushes the boat forward. So downstream speed = 7 + 3 = 10 km/hr. Upstream speed = B – S, because the current pushes against the boat. So upstream speed = 7 – 3 = 4 km/hr. The boat’s speed downstream is 10 km/hr.

Let boat speed in still water = B = 8 km/hr. Let stream speed = S = 3 km/hr. Downstream speed = B + S, because the current pushes the boat forward. So downstream speed = 8 + 3 = 11 km/hr. Upstream speed = B – S, because the current pushes against the boat. So upstream speed = 8 – 3 = 5 km/hr. The boat’s speed downstream is 11 km/hr.

Let boat speed in still water = B = 14 km/hr. Let stream speed = S = 2 km/hr. Downstream speed = B + S, because the current pushes the boat forward. So downstream speed = 14 + 2 = 16 km/hr. Upstream speed = B – S, because the current pushes against the boat. So upstream speed = 14 – 2 = 12 km/hr. The boat’s speed downstream is 16 km/hr.

Let boat speed in still water = B = 16 km/hr. Let stream speed = S = 5 km/hr. Downstream speed = B + S, because the current pushes the boat forward. So downstream speed = 16 + 5 = 21 km/hr. Upstream speed = B – S, because the current pushes against the boat. So upstream speed = 16 – 5 = 11 km/hr. The boat’s speed upstream is 11 km/hr.

Let boat speed in still water = B = 16 km/hr. Let stream speed = S = 2 km/hr. Downstream speed = B + S, because the current pushes the boat forward. So downstream speed = 16 + 2 = 18 km/hr. Upstream speed = B – S, because the current pushes against the boat. So upstream speed = 16 – 2 = 14 km/hr. The boat’s speed upstream is 14 km/hr.

Let boat speed in still water = B = 13 km/hr. Let stream speed = S = 6 km/hr. Downstream speed = B + S, because the current pushes the boat forward. So downstream speed = 13 + 6 = 19 km/hr. Upstream speed = B – S, because the current pushes against the boat. So upstream speed = 13 – 6 = 7 km/hr. The boat’s speed upstream is 7 km/hr.

Let boat speed in still water = B = 10 km/hr. Let stream speed = S = 2 km/hr. Downstream speed = B + S, because the current pushes the boat forward. So downstream speed = 10 + 2 = 12 km/hr. Upstream speed = B – S, because the current pushes against the boat. So upstream speed = 10 – 2 = 8 km/hr. The boat’s speed downstream is 12 km/hr.

Let boat speed in still water = B = 9 km/hr. Let stream speed = S = 7 km/hr. Downstream speed = B + S, because the current pushes the boat forward. So downstream speed = 9 + 7 = 16 km/hr. Upstream speed = B – S, because the current pushes against the boat. So upstream speed = 9 – 7 = 2 km/hr. The boat’s speed downstream is 16 km/hr.

Let boat speed in still water = B = 12 km/hr. Let stream speed = S = 3 km/hr. Downstream speed = B + S, because the current pushes the boat forward. So downstream speed = 12 + 3 = 15 km/hr. Upstream speed = B – S, because the current pushes against the boat. So upstream speed = 12 – 3 = 9 km/hr. The boat’s speed downstream is 15 km/hr.

Let boat speed in still water = B = 19 km/hr. Let stream speed = S = 5 km/hr. Downstream speed = B + S, because the current pushes the boat forward. So downstream speed = 19 + 5 = 24 km/hr. Upstream speed = B – S, because the current pushes against the boat. So upstream speed = 19 – 5 = 14 km/hr. The boat’s speed upstream is 14 km/hr.

Let boat speed in still water = B = 13 km/hr. Let stream speed = S = 5 km/hr. Downstream speed = B + S, because the current pushes the boat forward. So downstream speed = 13 + 5 = 18 km/hr. Upstream speed = B – S, because the current pushes against the boat. So upstream speed = 13 – 5 = 8 km/hr. The boat’s speed downstream is 18 km/hr.

Let boat speed in still water = B = 14 km/hr. Let stream speed = S = 8 km/hr. Downstream speed = B + S, because the current pushes the boat forward. So downstream speed = 14 + 8 = 22 km/hr. Upstream speed = B – S, because the current pushes against the boat. So upstream speed = 14 – 8 = 6 km/hr. The boat’s speed upstream is 6 km/hr.

Let boat speed in still water = B = 13 km/hr. Let stream speed = S = 7 km/hr. Downstream speed = B + S, because the current pushes the boat forward. So downstream speed = 13 + 7 = 20 km/hr. Upstream speed = B – S, because the current pushes against the boat. So upstream speed = 13 – 7 = 6 km/hr. The boat’s speed upstream is 6 km/hr.

Let boat speed in still water = B = 10 km/hr. Let stream speed = S = 6 km/hr. Downstream speed = B + S, because the current pushes the boat forward. So downstream speed = 10 + 6 = 16 km/hr. Upstream speed = B – S, because the current pushes against the boat. So upstream speed = 10 – 6 = 4 km/hr. The boat’s speed upstream is 4 km/hr.