A person travels three equal distance at a speed of x km/hr, y km/hr and z km/hr respectively. What is the average speed for the whole journey ?
A
$$\frac{{xyz}}{{3\left( {xy + yz + zx} \right)}}$$ km/hr
B
$$\frac{{xyz}}{{\left( {xy + yz + zx} \right)}}$$ km/hr
C
$$\frac{{\left( {xy + yz + zx} \right)}}{{xyz}}$$ km/hr
D
$$\frac{{3xyz}}{{\left( {xy + yz + zx} \right)}}$$ km/hr
Correct Answer: $$\frac{{3xyz}}{{\left( {xy + yz + zx} \right)}}$$ km/hr
Let each distance be equal to dThen, 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 :
$$\eqalign{ & = \left{\text{km/hr}} \cr & = \frac{{3xyz}}{{\left( {xy + yz + zx} \right)}}{\text{ km/hr}} \cr} $$
