Question

A train travels the first 30 km of 120 kilometre track with a uniform speed of 30 kilometre per hour what should be the speed of train to cover the remaining distance of the track so that its average speed is 60 kilometre per hour for the entire trip .


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Answer 1

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distance d1 = 30 km,      v1 = 30 kmph

   => time taken = t1 = d1/v1 = 1 hour

So distance remaining = d2 = 120 - d1 = 90 km

let speed to cover distance d2 = v2  kmph

   => time taken = d2/v2 = 90/v2  hours

average speed = total distance / total duration of time

               60 kmph = 120 km / [1 hour + 90 / v2  hours]

       =>  1 = 2 / [ 1 + 90 / v2 ]

       =>  v2 = 90 kmph

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another way:

   as the total distance = 120 km

   average speed = 60 kmph 

       => total time duration = 120 / 60 = 2 hours

 

   time taken for the first 30 km =  30 km /30 kmph = 1 hours

   Hence, time remaining to cover the remaining 90 km = 2 hrs - 1 hrs = 1 hour

   => speed during 90 km  = 90 kmph

Answer 2

Answer:

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