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A boat goes 30km upstream and 44km downstream in 10 hours. In 13 hours, it can go 40km upstream and 55km down-stream. Determine the speed of the stream

Let the speed of the boat be x and the speed of the strean be y Then speed of the boat in upstream = (x-y) kmph The speed of the boat in downstream = (x+y) kmph Then 30/(x-y) + 44/(x+y) = 10Let 1/(x-y) = a and 1/(x+y) = bIt implies 30a +44b = 10.......(i) Similarly 40a+55b = 13........(ii) Multiplying (i) by 4 and (ii) by 3 we get120a + 176b = 40...........(iii) 120a + 165b = 39..........(iv)Subtracting (iv) from (iii) we get 44b = 12 Hence b = 1/11Putting b in (i) we get 30a + 4 = 10 Hence a = 1/5Now b = 1/x+y = 1/11or x+y = 11..........(v)and a = 1/x-y = 1/5or x-y = 5...........(vi)Adding (v) and (vi) we get 2x = 16 Hence x = 8Putting x in (v) we get8+y = 11 Hence y = 3 Hence the speed of the boat = 8kmph and speed of the stream = 3kmph