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motorcycles drives A to B with a uniform speed of 30 km and returns back with the speed of 20 km find its average speed.
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Answer :

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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