Question

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 1

$average \: speed = \frac{total \: distance}{total \: time}$
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..

Answer 2

Average speed =total distance/total time
First hour it travelled 30kms and second hour we don't know the speed so let assume speed is 'x' km/h
60= 120/30km/30km/h +90km/X km/h
Then
60 = 120/1+90/X
60(1+90/X)=120
1+90/X=2
90/X=1
X=90
So speed is 90km/h