Question

Q3) On a 120km long track, a train travel's first 30km and an average speed of 30km/hr. How fast must tha train travel next 90km so that average speed for entire trip becomes 60km/hr

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