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Q. Suppose you drive to Delhi ($200\, km$ away) at $400\, km/hr$ and return at $200\, km/hr$. What is yours average speed for the entire trip?

UPSEEUPSEE 2016

Solution:

Average speed $=\frac{\text { Total Distance }}{\text { Total Time }}$
$=\frac{d_{1}+d_{2}}{t_{1}+t_{2}}$
$=\frac{200+200}{\frac{200}{400}+\frac{200}{200}}$
$\left[\because t_{1}=\frac{d_{1}}{v_{1}}\right.$ and $\left.t_{2}=\frac{d_{2}}{v_{2}}\right]$
$=\frac{400}{\frac{1}{2}+1}$
$=\frac{400}{\frac{1+2}{2}}=\frac{800}{3}=266.66 \simeq 267\, km / h$
i.e.it is less than $300\, km / h$.