Question

A man covered 1/4th of the total distance at 16 kmph and the remaining distance at 24 kmph. What is his average speed for the whole journey

Answer 1

Given:

A man covered 1/4th of the total distance at 16 kmph and the remaining distance at 24 kmph.

To find:

Average speed for whole journey

Calculation:

Average speed is defined as the total distance divided by the total time taken to cover the entire distance.

Let total distance be d ;

$\sf{avg. \: v = \dfrac{total \: distance}{total \: time} }$

$= > \sf{avg. \: v = \dfrac{d}{t1 + t2} }$

$= > \sf{avg. \: v = \dfrac{d}{ (\dfrac{d1}{v1} )+ (\dfrac{d2}{v2}) } }$

$= > \sf{avg. \: v = \dfrac{d}{ (\dfrac{ \frac{d}{4} }{16} )+ (\dfrac{ \frac{3d}{4} }{24}) } }$

$= > \sf{avg. \: v = \dfrac{d}{ (\dfrac{d}{64} )+ (\dfrac{d}{32}) } }$

$= > \sf{avg. \: v = \dfrac{1}{ (\dfrac{1}{64} )+ (\dfrac{1}{32}) } }$

$= > \sf{avg. \: v = \dfrac{1}{ (\dfrac{1 + 2}{64} ) } }$

$= > \sf{avg. \: v = \dfrac{64}{ 3 } }$

$= > \sf{avg. \: v = 21.33 \: kmph }$

So, final answer is:

$\boxed{ \red{\rm{avg. \: v = 21.33 \: kmph }}}$