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A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?1. 8 : 32. 3 : 23. 3 : 14. Cannot be determined |
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Answer» Correct Answer - Option 1 : 8 : 3 Given: Boat takes time to cover a certain distance upstream = 8 hours 48 minutes Boat takes time to cover the same distance downstream = 4 hours Formula Used: Speed = Distance/Time Calculation: Let speed of boat in still water be x km/h Let speed of current be y km/h Let the certain distance be D km Upstream speed = (x – y) km/h Downstream speed = (x + y) km/h 8 hours 48 minutes = 44/5 hours D/(x + y) = 4 .....(i) D/(x – y) = 44/5 .....(ii) Dividing equation (i) by (ii) \(⇒ \frac{{\frac{D}{{\left( {x + y} \right)}}}}{{\frac{D}{{\left( {x\;-{\rm {y}}} \right)}}}} = \;\frac{4}{{\frac{{44}}{5}}}\) ⇒ (x – y)/(x + y) = (4 × 5)/44 ⇒ 44 (x – y) = 20 (x + y) ⇒ 44x – 44y = 20x + 20y ⇒ 44x – 20x = 20y + 44y ⇒ 24x = 64y ⇒ x/y = 64/24 ⇒ x/y = 8/3 ⇒ x : y = 8 : 3 ∴ The ratio between the speed of the boat and speed of the water current is 8 : 3 |
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