What is the average speed for the total journey? Full question the description box below as an image.

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Answer 1 · 2018-01-04T06:41:03

The answer is #S=(160x)/(80+x)#

Let the total distance of the journey be #=d km#

Haf the distance is #=d/2km#

Average speed for the first half is #=80kmh^-1#

The time taken for this first half is #t_1=(d/2)/(80)=(d/160) h#

Average speed for the second half is #=xkmh^-1#

The time taken for this second half is #t_2=(d/2)/(x)=(d/(2x)) h#

The total time is #t=t_1+t_2=d/160+d/(2x)=d(1/160+1/(2x))#

#=d/2(1/80+1/x)=d/2((80+x)/(80x))#

The #"average speed"="total distance"/"total time"#

#barv=(d)/(d/2((80+x)/(80x)))=(160x)/(80+x)#

#S=(160x)/(80+x)#