In a stream running at 3 km/h, a motorboat goes 12 km upstream and back to the starting point in 60 min. find the speed of the motorboat in still water. (in km/h)
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 3(4 + √(17))
| Understanding | Application |
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Speed in upstream = speed of the boat in still water - speed of the stream Speed in downstream = speed of the boat in still water + speed of the stream. |
Let the speed of boat in still water be 'v' km/h Total time taken by boat = time taken in upstream + time taken in downstream ⇒ 1 = 12 / (v - 3) + 12 / (v + 3) ⇒ 1 / 12= 1 / (v - 3) + 1 / (v + 3) ⇒ 1 / 12= (v + 3 + v - 3) / (v + 3)(v - 3) ⇒ 1 / 12= 2v / v2 - 9 ⇒ v2 - 9 = 24v ⇒ v2 - 24v - 9 = 0 The roots of the quadratic equations are 3(4 + √17) and 3(4 - √17) As speed cannot be negative so the only possible solution will be 3(4 + √17) |