Question

A train travels the first 30km of
120km track with a uniform
speed of
of 30km/hr what should be
the speed of the train to cover the
remaining
distance of track so that the avg. speed will be 60km/hr for the entire trip.​

Answer 1

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