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

AB=BC=CD

(i) Time taken by car to cover from A to B and then from B to C = $\frac{x}{40}$+$\frac{x}{60}$ hr

Average speed from A to D(Distance/Time)

= $\frac{3x}{{\displaystyle \frac{x}{40}}+{\displaystyle \frac{x}{60}}}$

=$\frac{3}{{\displaystyle \frac{6+8}{240}}}$

=$\frac{3\times 240}{14}$

=51.4 kmph

(ii) Time taken by car to cover from A to B and then from B to C 

= $\frac{x}{40}$+$\frac{x}{60}$

Average speed from A to C

=$\frac{2x}{{\displaystyle \frac{x}{40}}+{\displaystyle \frac{x}{60}}}$

=$\frac{2}{{\displaystyle \frac{3+2}{120}}}$

= 48 kmph