ABCD is a straight line such that AB = BC = CD. A car travelled with a speed of 40kmph from A to B and with speed of 60kmph from B to D. Its average speeds (in kmph) in the journey (i) from A to C and    (ii) from A to D are                    

Given that a car travelled from A to B i.e. AB = s

With speed ${\text{v}}_{\text{1}}=40\text{kmph}$

From B to D

BD = 2s

With speed ${\text{v}}_2=60\text{kmph}$

$\text{AB}=\text{BC}=\text{CD}$

i)${\text{v}}_{\text{Avg}}=\left[\text{AtoC}\right]=\frac{{\text{2v}}_{\text{1}}{\text{v}}_{\text{2}}}{{\text{v}}_{\text{1}}+{\text{v}}_{\text{2}}}$

$=\frac{2\left(40\right)\left(60\right)}{40+60}=\frac{2\times 2400}{100}$

${\text{v}}_{\text{Avg}}=48\text{kmph}$

ii) ${\text{v}}_{\text{Avg}}=\left[\text{AtoD}\right]=\frac{3\text{s}}{\frac{\text{s}}{40}+\frac{2\text{s}}{60}}$

$=\frac{3\text{s}}{\left[\frac{1}{40}+\frac{2}{60}\right]}=\frac{3}{\frac{3+4}{120}}$

$=\frac{3\times 120}{7}=\frac{360}{7}=51.4\text{km/h}$

${\text{v}}_{\text{Avg}}=51.4\text{kmph}\left(\text{AtoD}\right)$