Question

PLEASE HELP!! NO FAKE ANSWERS!!PLEASE!!On a 120km track , a train travels the first 30km with a uniform speed of 30km/h. How fast must the train travel the next 90km so as to average 60km/h 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

Answer 2

V average = (vf + vi) / 2

60km/hr = (vf + 30km/hr) / 2

Multiplying by 2 to both sides :

120km/hr = vf + 30km/hr

subtracting 30km/hr from both sides.

90km/hr = vf