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) \[\frac{x{{v}_{1}}+y{{v}_{2}}}{xy\,({{v}_{1}}+{{v}_{2}})}km/h\]
Correct Answer: A
Solution :
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 \[\text{=}\frac{\text{Distance}}{\text{Time}}\,=\,\left( \frac{x+y}{x/{{v}_{1}}+y/{{v}_{1}}} \right)\] \[=\frac{{{v}_{1}}{{v}_{2}}\,(x+y)}{x{{v}_{2}}+\,\,y{{v}_{1}}}km/h\]
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