Question
A boat covers 12 km upstream and 20km downstream in 4
hours while it covers 20km upstream and 12 km downstream in 4*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 12/x+20/y= 4 ………….(i) 20/x+12/y=4 1/2…………………….(ii) Adding (i) and (ii), we get 32(1/x+1/y)=17/2…………..(iii) Subtract (i) from (ii), we get 8(1/x-1/y)=1/2…………..(iv) Adding (iii) and (iv), we get 2/x=17/64+ 1/16 2/x = 21/64 x = 128/21 km/hr Now, 21/128 - 1/y = 1/16 y = 128/13 km/hr Now, rate of current = 1/2(128/13-128/21) =1.8 Km/hr
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