Answer:
6 km/h
Explanation:
For the fist half we must have a distance travelled and the time that this distance was travelled in, we will call this d1, and t1. For the second half we must also have a distance and a time: d2 and t2.
If we say that the total distace was 'x'
[tex]d1=\frac{1}{2}x[/tex]
[tex]d2=\frac{1}{2}x[/tex]
Now, let's find t1 and t2.
for the fist half the horse was traveling at a velocity of 12 km/h, using [tex]time =\frac{distance}{velocity}[/tex]
We have for t1:
[tex]t1=\frac{\frac{1}{2}x}{12km/h} = \frac{x}{24}[/tex]
And for t2, since the horse now is traveling at 4 km/h:
[tex]t2=\frac{\frac{1}{2}x}{4km/h}=\frac{x}{8}[/tex]
And finally we can find the average velocity, using the formula:
[tex]velocity=\frac{totaldistance}{totaltime}[/tex]
Thus, replacing the values we found:
[tex]v=\frac{d1+d2}{t1+t2}=\frac{\frac{1}{2}x+\frac{1}{2}x}{\frac{x}{24}+\frac{x}{8}} =\frac{x}{\frac{4x}{24}} =\frac{24}{4} =6km/h[/tex]
