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Exaple 19 :,A boat goes 30 kmupstream and/44 km downstream in10 hours. In 13 hours, it can go40 km upstream and 55 kmdown-stream. Determine the speedof the stream and that of the boat instill water.. |
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Answer» Let the speed of the stream be = u kmphlet the speed of the boat be = v kmph speed upstream will be = v - u kmph speed downstream will be = v + u kmph 30 km upstream in time duration = 30 / (v - u) hrs44 km down stream in time duration = 44 / (v + u) hrs 44 / (v + u) + 30 / (v -u) = 10 hrs --- (1) Similarly, 40 /(v - u) + 55 / (v +u) = 13 hrs Multiply with 3/4: 30/(v-u) + 165 / 4(v+u) = 39/4 --- (2) Now (1) - (2) => [44 - 165/4] / (v+u) = 10 - 39/4 = 1/4 => v + u = 11 --- (3)Substitute this in (1) to get: 44/11 + 30/(v-u) = 10 => v - u = 30/6 = 5 --- (4) Solving (3) and (4) , we get : v = 8 kmph and u = 3 kmph |
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