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 $"average speed"="total distance"/"total time"$

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

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