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

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1 Answer
Jan 4, 2018

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

Explanation:

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)