A) \[\frac{1}{2}\sqrt{{{\upsilon }_{1}}{{\upsilon }_{2}}}\]
B) \[\frac{5{{\upsilon }_{1}}{{\upsilon }_{1}}}{3{{\upsilon }_{1}}+2{{\upsilon }_{2}}}\]
C) \[\frac{2{{\upsilon }_{1}}{{\upsilon }_{2}}}{{{\upsilon }_{1}}+{{\upsilon }_{2}}}\]
D) \[\frac{{{\upsilon }_{1}}+{{\upsilon }_{2}}}{2}\]
Correct Answer: A
Solution :
Let total distance covered \[=s\] \[{{t}_{1}}=\frac{(2/5)s}{{{\upsilon }_{1}}}\]and \[{{t}_{2}}=\frac{(3/5)s}{{{\upsilon }_{2}}}\] \[Average\text{ }speed=\frac{total\text{ }distance}{total\text{ }time}\] \[\upsilon =\frac{s}{{{t}_{1}}+{{t}_{2}}}\] Or \[\upsilon =\frac{s}{\frac{2s}{5{{\upsilon }_{1}}}+\frac{3s}{5{{\upsilon }_{2}}}}\] Hence, \[\upsilon =\frac{5{{\upsilon }_{1}}{{\upsilon }_{2}}}{2{{\upsilon }_{2}}+3{{\upsilon }_{1}}}\]
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