- $$\frac{{xyz}}{{3\left( {xy + yz + zx} \right)}}$$ km/hr
- $$\frac{{xyz}}{{\left( {xy + yz + zx} \right)}}$$ km/hr
- $$\frac{{\left( {xy + yz + zx} \right)}}{{xyz}}$$ km/hr
- $$\frac{{3xyz}}{{\left( {xy + yz + zx} \right)}}$$ km/hr
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Answer: Option 4
Let each distance be equal to d Then, total distance travelled = 3d Total time taken : $$\eqalign{ & = \left( {\frac{d}{x} + \frac{d}{y} + \frac{d}{z}} \right){\text{hr}} \cr & = \frac{{d\left( {xy + yz + zx} \right)}}{{xyz}}{\text{ hr}} \cr} $$ ∴ Average speed : $$\eqalign{ & = \left[ {3d \times \frac{{xyz}}{{d\left( {xy + yz + zx} \right)}}} \right]{\text{km/hr}} \cr & = \frac{{3xyz}}{{\left( {xy + yz + zx} \right)}}{\text{ km/hr}} \cr} $$
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