Physics-
General
Easy

Question

A motion boat covers a given distance in 6 h moving down stream of a river. It covers the same distance in 10 h moving upstream. The time (in hour) it takes to cover the same distance in still water is

  1. 6  
  2. 7.5  
  3. 10  
  4. 15  

The correct answer is: 7.5


    Let v subscript w end subscript be velocity of water and v subscript b end subscript be the velocity of motor boat in still water. If x blankis the distance covered, then as per question
    x equals open parentheses v subscript b end subscript plus v subscript w end subscript close parentheses cross times 6 equals left parenthesis v subscript b end subscript minus v subscript w end subscript right parenthesis cross times 10
    On solving, v subscript w end subscript equals v subscript b end subscript divided by 4
    therefore blank x equals open square brackets v subscript b end subscript plus v subscript b end subscript divided by 4 close square brackets cross times 6 equals 7.5 v subscript b end subscript
    Time taken by motor boat to cross the same distance in still water is
    t equals fraction numerator x over denominator x subscript b end subscript end fraction equals fraction numerator 7.5 over denominator v subscript b end subscript end fraction equals 7.5h

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