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that- 2 and v2 are two of its zeros.12. A motorboat can travel 30 km upstream and 28 km downstream in 7 hours.It can travel 21 km upstream and return in 5 hours. Find the speed of theboat in still water & that of the stream. |
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Answer» This kind of questions follows the same pattern: Let the speed of the boat in still water = xkm/hr. Let the speed of the stream = ykm/hr. Speed upstream = x - y. Speed Downstream = x + y. Now, Given that boat can travel 30km upstream and 28km downstream in 7 hours. 30/x-y + 28/x+y = 7 Let 1/x - y = a and 1/x + y = b 30a + 28b = 7 ---------------------------- (1). Also, Given that it can travel 21 km upstream and return in 5 hours. 21/x - y + 21/x + y = 5 Let 1/x - y = a and 1/x + y = b 21a + 21b = 5 ------------------------ (2) On solving (1) * 21 & (2) * 28, we get 630a + 588b = 147 588a + 588b = 140-----------------------------42a = 7 a = 1/6. Substitute a = 6 in (1), we get 30a + 28b = 7 30(1/6) + 28b = 7 5 + 28b = 7 28b = 7 - 5 28b =2 b = 2/28 b = 1/14. We know that, a = 1/x - y 1/6 = 1/x - y x - y = 6 ----------- (3) We know that, b = 1/x + y 1/14 = 1/x + y x + y = 14 ------------ (4). On solving (3) & (4), we get x + y = 14 x - y = 6 ------------ 2x = 20 x = 10 Substitute x = 10 in (4), we get x + y = 14 10 + y = 14 y = 14 - 10 y = 4. Therefore the speed of the boat in still water = 10km/hr. Therefore the speed of the stream = 4km/hr. |
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