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Question

A car moves a distance of 200 blank m. It covers first half of the distance at speed 60 blank k m h to the power of negative 1 end exponent and the second half at speed v. If the average speed is 40 blank k m h to the power of negative 1 end exponent, the value of v is

  1. 30 blank k m h to the power of negative 1 end exponent  
  2. 13 blank k m h to the power of negative 1 end exponent  
  3. 60 blank k m h to the power of negative 1 end exponent  
  4. 40 blank k m h to the power of negative 1 end exponent  

The correct answer is: 30 blank k m h to the power of negative 1 end exponent


    Time taken by the car to cover first half of the distance is
    t subscript 1 end subscript equals fraction numerator 100 over denominator 60 end fraction
    Time taken by the car to cover speed half of the distance is
    t subscript 2 end subscript equals fraction numerator 100 over denominator v end fraction
    Average speed , v subscript a v end subscript equals fraction numerator T o t a l blank d i s t a n c e blank t r a v e l l e d over denominator T O t a l blank t i m e blank t a k e n end fraction
    v subscript a v end subscript equals fraction numerator 100 plus 100 over denominator t subscript 1 end subscript plus t subscript 2 end subscript end fraction rightwards double arrow 40 equals fraction numerator 200 over denominator fraction numerator 100 over denominator 60 end fraction plus fraction numerator 100 over denominator v end fraction end fraction
    fraction numerator 1 over denominator 60 end fraction plus fraction numerator 1 over denominator v end fraction equals fraction numerator 1 over denominator 20 end fraction rightwards double arrow fraction numerator 1 over denominator v end fraction equals fraction numerator 1 over denominator 20 end fraction minus fraction numerator 1 over denominator 60 end fraction
    fraction numerator 1 over denominator v end fraction equals fraction numerator 2 over denominator 60 end fraction equals fraction numerator 1 over denominator 30 end fraction
    v equals 30 k m blank h to the power of negative 1 end exponent

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