Question

Rahul travels at a speed of 30km/h while going to school. While coming back, he travels at a speed of 40km/h (due to less traffic). What is his average speed?

- Don't spam ^^" ​

Answer 1

Answer:

the average speed is 35km/h

Answer 2

Answer:

• Speed (v₁) = 30 km/h
• Speed (v₂) = 40 km/h

$\footnotesize\implies \: \bigg[Speed \bigg]_{(Average)} = \dfrac{Total \: Distance }{Total \: time }$

$\footnotesize\implies \: \bigg[Speed \bigg]_{(Average)} = \dfrac{ x_{1} + x_{2} }{t_{1} +t_{2} }$

$\footnotesize\implies \: \bigg[Speed \bigg]_{(Average)} = \dfrac{ x_{1} + x_{2} }{ \frac{x_{1}}{v_{1}} + \frac{x_{2}}{v_{2}} }$

Distance travelled while going to school and while comming back will be same.

• x = x₁ = x₂

$\footnotesize\implies \: \bigg[Speed \bigg]_{(Average)} = \dfrac{ 2x }{ \frac{x}{v_{1}} + \frac{x}{v_{2}} }$

$\footnotesize\implies \: \bigg[Speed \bigg]_{(Average)} = \dfrac{ 2 }{ \frac{1}{v_{1}} + \frac{1}{v_{2}} }$

$\footnotesize\implies\: \bigg[Speed \bigg]_{(Average)} = \dfrac{ 2 }{ \frac{v_{1} + v_{2}}{v_{1}.v_{2}} }$

$\footnotesize\implies \: \bigg[Speed \bigg]_{(Average)} = \dfrac{ 2 v_{1}v_{2}}{ v_{1} + v_{2} }$

$\footnotesize\implies \: \bigg[Speed \bigg]_{(Average)} = \dfrac{ 2 \times 30 \times 40}{ 30 + 40 }$

$\footnotesize\implies \: \bigg[Speed \bigg]_{(Average)} = \dfrac{ 2 \times 30 \times 40}{ 30 + 40 }$

$\footnotesize\implies \: \bigg[Speed \bigg]_{(Average)} = \dfrac{ 2400}{ 70 }$

$\footnotesize\implies\: \bigg[Speed \bigg]_{(Average)} = \dfrac{ 240}{ 7 }$

$\footnotesize\implies \: \underline{\boxed{\bf{\red{\bigg[Speed \bigg]_{(Average)} = 34.28 \:km/h }}}}$