Question

a train travels from delhi to chandigarh at a speed of 40 km per hour and then return back to chandigarh to delhi at a speed of 60km/hr . what is the average speed of the train for the round trip

Answer 1

let distance from delhi to chandigarh be 'x'
then in first case time = x / 40
in 2nd case time = x / 60; (time = distance /speed )
so avg. speed = total distance / time taken
::::》x+x/(x/40+x/60)
::::》avg. speed = 48 km /hr

Answer 2

ANSWER
========

Let the distance between Delhi and Chandigarh be = s

Speed of the train from Delhi to Chandigarh = 40km/h

Therefore , time ( t ) =

We know----

Speed = Distance travelled / Time


$40 \: km \: per \: hour \: = \: \frac{s}{t} \\ \\ t \: = \: \frac{s}{40}h$
Speed of train from Chandigarh to Delhi = 60km/h

Therefore , time =

$60 \: km \: per \: hour \: = \frac{s}{t} \\ \\ t \: = \: \frac{s}{60} h \\ \\ average \: speed = \frac{total \: distnce \: travelled}{total \: time} \\ \\ \: \: = \: \frac{s \: + \: s}{ \frac{s}{40} + \frac{s}{60} } \\ \\ \ = \frac{s + s}{ \frac{3s \: + \: 2s}{102} } \\ \\ = \: \frac{2s}{ \frac{5s}{120} } \\ \\ = 2s \: \times \frac{120}{5s} \\ \\ = 2 \: \times \: 24 \\ \\ = \: 48 \: km \: per \: hour$

ANS. The average speed of the train is 48km/h

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