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

let the speed of the boat in stream be xkm/h and ykm/h be the speed of stream

speed of boat in downstream = x+y

speed of boat in upstream = x-y

using 1st condition

30/ x-y + 44/ x+y = 10

22/ x+y + 15/ x-y = 5 --(1)

using 2nd condition

40/x-y + 55/x+y =13

11/x+y + 8/x-y=13/5 --(2)

multiplying eq--(2) by 2

we get,

22/x+y + 16/x-y =26/5 --(3)

subtracting eq(1) from eq(3)

22/ x+y + 15/ x-y = 5

- ( 22/x+y + 16/x-y = 26/5 )

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= - 1/x-y = -1/5

x-y = 5 --(4)

putting thisin eq (2)

11/x+y + 8/5=13/5

we get x+y = 11 --(5)

Adding eq (4) and eq (5)

x-y = 5

x+y = 11

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2x = 16

** x = 8**

put this in eq (5)

8 + y = 11

** y = 3**

speed of boat in downstream = x+y

= 8+3

**= 11**

speed of boat in upstream = x-y

= 8-3

** = 5**

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