Explanation :

Total distance = 10 + 12 = 22 km

∵ Time = $\dfrac{\text{Distance}}{\text{Speed}}$

Time taken to travel 10 km at an average speed of 12 km/hr = $T_1$ = $\dfrac{10}{12}$ hr

Time taken to travel 12 km at an average speed of 10 km/hr = $T_2$ = $\dfrac{12}{10}$ hr

∴ Total time taken = $T_1$ + $T_2$

                              = $ \left(\dfrac{10}{12}+\dfrac{12}{10}\right)$ hr

∵ Average speed = $\dfrac{\text{Distance}}{\text{Time}}$

= $\dfrac{22}{\left(\dfrac{10}{12}+\dfrac{12}{10}\right)}$

= $\dfrac{22\times120}{(10\times10)+(12\times12)} $

= $\dfrac{22 \times120}{244}$

= $ \dfrac{11 \times120}{122}$

= $\dfrac{11 \times60}{61}$

≈ 10.8 kmph

Explanation :

Given that, Distance = 8.5 km

and Relative speed = (5.5 - 5) kmph = .5 kmph (because they walk in the same direction.)

We know that,

Time = $\dfrac{\text{Distance}}{\text{Speed}}$

⇒ Time = $\dfrac{8.5}{.5}$ hr

⇒ Time = 17 hr