a boat takes 6 hours to travel 24 km upstream and 36km downstream and it takes 9 hours to travel 40 km upstream and 48 km downstre

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1. Answer 6,2

   Let the speed of the boat in still water be x km/hr

   Let the speed of the stream be y km/hr

   The speed of the boat downstream = (x+y) km/hr

   The speed of the boat upstream = (x−y) km/hr

   Time=

   Speed

   Distance

   6 hours to travel 8 km upstream and 32 km downstream,

   i. e 6=

   x−y

   8

   +

   x+y

   32

   (1)

   7 hours to travel 20 km upstream and 16 km downstream.

   i.e 7=

   x−y

   20

   +

   x+y

   16

   (2)

   Let

   x−y

   1

   =a and

   x+y

   1

   =b

   ∴6=8a+32b …(3)

   7=20a+16b …(4)

   On solving the equations, we get a=

   4

   1

   and b=

   8

   1

   x−y

   1

   =

   4

   1

   and

   x+y

   1

   =

   8

   1

   ⟹4=x−y

   ⟹8=x+y

   Add the above (2) eqn we get

   12=2x

   x=6 and y=2

   So, the speed of the boat in still water = 6 km/hr

   The speed of the stream = 2 km/hr

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