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Answer:

Let the speed of the boat =  x kmph

Given speed of the stream    4 kmph

Therefore Speed of the boat in  downstream =  (x+4) kmph

Speed of the boat in upstream =  (x-4) kmph

Time taken to travel 160 kms in downstream =  160/(x+4) hrs

Time taken to travel 160 kms in upstream = 160/(x-4) hrs

Total time taken to go and return =  {160/(x+4)} + {160/(x-4)}    = 9 hrs

Simplifying ,we get 160*(x-4)+160*(x+4) =  9(x+4)*(x-4)

that is 320x = 9*(x^2-16)  or   9x^2-320x -144 =0

Factorising the quadratic ,we get (x-36)*(9x+4) =0

Hence x =36 kmph.The negative answer for x is rejected as x cannot be negative.

Distance travelled by the boat in 4 hrs in downstream = 4*(x+4) = 4(36+4) = 160 kms

Distance travelled by the boat in 3 hrs in upstream = 3*(x-4) = 3(36-4)  =         96 kms

Therefore Difference in distance travelled =   160-96 = 64 kms

 

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