1.

On a 120 km track, a train travels the 1st 30 km at uniform speed of 30km/hr. How fast must the train travel the next 90 km to get average speed of 60 km/hr for the whole journey?

Answer»
average \: speed = \frac{total \: distance}{total \: time}
So,
The average speed is given=60km/h
Distance=120km
Let the time be x.
60 = \frac{120}{x}
x = \frac{120}{60} = 2hrs
From first PART of train journey,we have:-
Speed=30km/h
Distance=30km
Time=?
speed = \frac{distance}{time}
30 = \frac{30}{time}
time = \frac{30}{30 } = 1hrs
From,the SECOND part of journey we have:-
Speed =x
Distance =90KM/h
Time=?

s = \frac{d}{t} \\ x = \frac{90}{time } \\ time = \frac{90}{x}

We ,already know that total time TAKEN for trip =2hrs.
A/q
1 + \frac{90}{x} = 2 \\ \frac{90}{x} = 2 - 1 \\ \frac{90}{x} = 1 \\ x = 90

Hence,the train will COVER next 90km at speed of 90km/h..


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