A 36 km journey in an auto rickshaw requires 3 hours to complete. The time it takes to travel the same distance if its speed is raised by 4 km/h is ____ hour.

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A 36 km journey in an auto rickshaw requires 3 hours to complete. The time it takes to travel the same distance if its speed is raised by 4 km/h is 2.25 hour.It is given that a 36 km journey in an auto rickshaw requires 3 hours to complete.We know that two variables

x and y
  are said to be inversely proportional if and only if they are directly proportional to one another's reciprocal. If

x and y
  are two variables in inverse variations, then

x∝
      1
      y

⇒x=k
      1
      y

⇒x=
      k
      y
     
     ,        where k is proportianality constant

⇒xy=k                                                   ....(1)

Since it is given that distance covered by an auto rickshaw in 3 hours = 36 km.

∴Speed=
    
     36
    3
   
   =12 km/h.
  Therefore, the initial speed of an auto rickshaw was 12 km/h.Speed of the auto rickshaw if it is increased by 4 km/h is 16 km/h.Let the time taken to travel the same distance if its speed is raised by 4 km/h is

x.
  Then from the given data, we can draw the following table as,Since, on increasing the average speed, there will be a decrease in the time taken, therefore this is a case of inverse proportion. Thus,

12×3=16×x

⇒x=

12×3
          
           16

⇒x=2.25 hour

Therefore, the time taken to travel the same distance if its speed is raised by 4 km/h is 2.25 hour.

A 36 km journey in an auto rickshaw requires 3 hours to complete. The time it takes to travel the same distance if its speed is raised by 4 km/h is ____ hour.

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