• question_answer A car runs x km at an average speed of ${{v}_{1}}$ km/h and y km at an average speed of ${{v}_{2}}$ km/h. What is the average speed of the car for the entire journey? A)  $\frac{{{v}_{1}}{{v}_{2}}(x+y)}{x{{v}_{2}}+y{{v}_{1}}}km/h$ B)  $\frac{x{{v}_{2}}+y{{v}_{1}}}{{{v}_{1}}{{v}_{2}}(x+y)}km/h$ C)  $\frac{xy({{v}_{1}}+{{v}_{2}})}{x{{v}_{1}}+y{{v}_{2}}}km/h$ D)  $\frac{x{{v}_{1}}+y{{v}_{2}}}{xy\,({{v}_{1}}+{{v}_{2}})}km/h$

Time taken in the first journey $=\frac{x}{{{v}_{1}}}h$ Time taken in the second journey $=\frac{y}{{{v}_{2}}}h$ Total distance $=(x+y)$ km Total time $=\left( \frac{x}{{{v}_{1}}}+\frac{x}{{{v}_{2}}} \right)h$ $\therefore$ Average speed $\text{=}\frac{\text{Distance}}{\text{Time}}\,=\,\left( \frac{x+y}{x/{{v}_{1}}+y/{{v}_{1}}} \right)$ $=\frac{{{v}_{1}}{{v}_{2}}\,(x+y)}{x{{v}_{2}}+\,\,y{{v}_{1}}}km/h$