Answer:
Time taken by person to travel first
half length, \[{{t}_{1}}=\frac{\left( d/2 \right)}{{{\upsilon
}_{1}}}=\frac{d}{2{{\upsilon }_{1}}}\]
Time taken by person
to travel second half length, \[{{t}_{2}}=\frac{d/2}{{{\upsilon
}_{2}}}=\frac{d}{2{{\upsilon }_{2}}}\]
\[\therefore \] Total
time = \[{{t}_{1}}+{{t}_{2}}=\frac{d}{2}\left[ \frac{1}{{{\upsilon
}_{1}}}+\frac{1}{{{\upsilon }_{2}}} \right]=\frac{d\left( {{\upsilon
}_{1}}+{{\upsilon }_{2}} \right)}{2{{\upsilon }_{1}}{{\upsilon }_{2}}}\]
\[\therefore \] Mean
velocity or average velocity \[=\frac{d}{{{t}_{1}}+{{t}_{2}}}=\frac{2{{\upsilon
}_{1}}{{\upsilon }_{2}}}{\left( {{\upsilon }_{1}}+{{\upsilon }_{2}} \right)}\]
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