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Sagot :
Answer:
the average speed = 24 km/h
Explanation:
We can find the average speed by using this formula:
[tex]\boxed{\overline{v}=\frac{\Sigma s}{\Sigma t} }[/tex]
where:
- [tex]\overline{v}=\text{average speed}[/tex]
- [tex]\Sigma s=\text{total distance}[/tex]
- [tex]\Sigma t=\text{total time}[/tex]
Let:
the distance between A and B = x km
Given:
- [tex]\text{distance from A to B}=x\ km[/tex]
- [tex]\text{speed from A to B}=30\ km/h[/tex]
- [tex]\text{distance from B to A}=x\ km[/tex]
- [tex]\text{speed from B to A}=20\ km/h[/tex]
Since the formula for time:
[tex]\boxed{time(t)=\frac{distance(s)}{speed(v)} }[/tex]
Then:
- [tex]\displaystyle \text{time from A to B}=\frac{x}{30} \ h[/tex]
- [tex]\displaystyle \text{time from A to B}=\frac{x}{20} \ h[/tex]
Hence:
[tex]\begin{aligned}\overline{v}&=\frac{\Sigma s}{\Sigma t}\\\\&=\frac{x+x}{\frac{x}{30} +\frac{x}{20} } \\\\&=\frac{2x}{\frac{2x+3x}{60} } \\\\&=2x\times\frac{60}{5x} \\\\&=\bf 24\ km/h\end{aligned}[/tex]
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