# On a 120km track, a train travels the first 30 km at a uniform speed of 30km/hr. How fast must the train travel the next 90 km so as to average 60 km/hr for the entire trip?

2
by ayeshaoct

2015-05-16T17:32:15+05:30
A train travels 120km totally and at first 30km it travels at a uniform speed of 30km/hr then it has to travel 90km more at totl average of 60km/hr so as 120-30=90and then it has to travel at average of 90km/hr
2015-05-17T15:30:03+05:30

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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

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