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A boat can row 3 times as fast in downstream than in upstream. In still water the boat covers a distance of 50 m in 5 seconds. Calculate the time the boat will take to cover a distance of 45 km downstream.1. 180 minutes2. 120 minutes3. 100 minutes4. 50 minutes5. 45 minutes |
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Answer» Correct Answer - Option 4 : 50 minutes Given: Speed downstream is 3 times speed upstream. In still water boat goes 50 m in 5 seconds. Concept: Speed downstream is sum of the speed of boat in still water and speed of stream Speed upstream is difference of the speed of boat in still water and speed of stream. To convert hours to minutes we have to multiply by 60 Formula: Speed = distance/time Time = distance/speed Speed in m/s × 18/5 = speed in km/h Calculation: Speed of boat in still water = 50/5 = 10 m/s Let the speed of stream be x m/s Speed during downstream = (10 + x) km/h Speed during upstream = (10 – x) km/h 3 × (10 – x) = (10 + x) ⇒ (10 – 3x) = (10 + x) ⇒ 3x + x = 30 – 10 ⇒ 4x = 20 ⇒ x = 5 Speed downstream = 10 + 5 = 15 m/s Speed downstream = 15 × (18/5) = 54 km/h Time to cover 45 km = 45/54 = (5/6) hours Time taken to cover 45 km = (5/6)× 60 = 50 mins ∴ Time to cover the distance downstream is 50 minutes |
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