Physics-
General
Easy

Question

A boat takes two hours to travel 8 km and back in still water. If the velocity of water 4 k m h to the power of negative 1 end exponent, the time taken for going ups tream 8km and coming back is

  1. 2h  
  2. 2 h 40 min  
  3. 1 h 20 min  
  4. Cannot be estimated with the information given  

The correct answer is: 2 h 40 min


    Boat covers distance of 16 km in a still water in hours
    i e blank v subscript B end subscript equals fraction numerator 16 over denominator 2 end fraction equals8k m h to the power of negative 1 end exponent
    Now, velocity of water
    v subscript W end subscript equals 4 k m h to the power of negative 1 end exponent
    Time taken for going upstream
    t subscript 1 end subscript equals fraction numerator 8 over denominator v subscript B end subscript minus v subscript w end subscript end fraction equals fraction numerator 8 over denominator 8 minus 4 end fraction equals 2h
    (As water current oppose the motion of boat) Time taken for going downstream
    t subscript 2 end subscript equals fraction numerator 8 over denominator v subscript B end subscript plus v subscript w end subscript end fraction equals fraction numerator 8 over denominator 8 plus 4 end fraction equals fraction numerator 8 over denominator 12 end fractionh
    (As water current helps the motion of boat)
    therefore Total time equals t subscript 1 end subscript plus t subscript 2 end subscript
    equals open parentheses 2 plus fraction numerator 8 over denominator 12 end fraction close parenthesesh=2 h 40 min

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