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In a stream running at 3 km/h, a motorboat goes 8 km upstream and back again to the starting point in 120 minutes. What is the speed of the motorboat in still water ?
- A8 kmh-1
- B9 kmh-1
- C10 kmh-1
- D11 kmh-1
Correct answer: B
Discussion 1
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CCommunity
9 kmh-1
Let the speed of the motorboat be V khm-1
∴ 8/V+3 + 8/V - 3 = 2
8V - 24 + 8V + 24/V² - 9
16V/V² - 9 = 2
∴ 2V² - 18 = 16V
V² - 9V + V - 9 = 0
V(V-9) + 1(V-9) = 0
(V + 1) (V - 9) = 0
∴ V = 9 - 1, (-ve not possible )
∴ V = 9 khm-1
Let the speed of the motorboat be V khm-1
∴ 8/V+3 + 8/V - 3 = 2
8V - 24 + 8V + 24/V² - 9
16V/V² - 9 = 2
∴ 2V² - 18 = 16V
V² - 9V + V - 9 = 0
V(V-9) + 1(V-9) = 0
(V + 1) (V - 9) = 0
∴ V = 9 - 1, (-ve not possible )
∴ V = 9 khm-1