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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.
Who answers first and the correct will be marked as brainiest and given 15pts​


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]