A bot covers 14 kmh in upstream and 20 kmh downstream in 7 hours. Also it covers 22 kmh upstream and 34 kmh downatream in 10 hours. Find the speed of the boat in still water and of that the stream.
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Answer:
here is ur answer hope it was help full
let the speed of a boat in still water = x km/h
and speed of the stream =y km/hr
= speed of boat in upstream=(x-y) km /hr and
=speed of boat in downstream=(x+y)km/hr
we know that ,
time =distance /speed
according to the conditions we get
=14/(x -y) + 20 / (x+ y) = 7 ....(1)
=22/(x -y) + 34 /x + y = 10
=11/(x-y) + 17/x + y = 5 ....(2)
let 1/x + y - m and 1/ x - y = n ,we get
=14m + 20 n = 7(3)
=11m + 17 n = 5.( 4)
multiply equation ( 3) by 11 and (4) by 14, we get
=154 m + 220n-77.(5)
=154m + 238n- 70(6)
= subtract (5) from (6) , we get
=18 n = -7
=n = -7/18
=put n =-7/18 in (3) ,we get
=14m + 20 (-7)/18= 7
=m=133/126
=1/x+ y =133/126 and 1/x-y = -7/18
=x +y =126/133 and x-y = -18/7
=adding both the equations ,we get
=x = -103/133 and y =234/133
=But speed of the boat in still water can't be negative ..just for reference
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