Question
A boat covers 32 km upstream and 40km downstream in 8
hours while it covers 40km upstream and 32 km downstream in `8 1/2` hours. What is the velocity of current?Solution
Let the speed of upstream be x km/hr Speed of downstream = y km/hr 32/x + 40/y = 8 ………….(i) 40/x + 32/y = 8(1/2) …………………….(ii) Adding (i) and (ii), we get 72(1/x + 1/y) = 33/2 …………..(iii) Subtract (i) from (ii), we get 8(1/x - 1/y) = 1/2 …………..(iv) Adding (iii) and (iv), we get 2/x = (33/144) + (1/16) 2/x = 42/144 x = 48/7 km/hr Now, 7/48 - 1/y = 1/16 y = 12 km/hr Now, rate of current = 1/2(12 - 48/7) = 18/7 km/hr = 2(4/7) km/hr
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