One third of a certain journey is covered at the speed of 80 km/hr one fourth of the journey at the speed of 50 km/hr and the rest at the speed of 100 km/hr what will be the average speed (in km/hr) for the whole journey?

$$\eqalign{ & {\text{Average speed}} = \frac{{{\text{Total Journey}}}}{{{\text{Time Taken}}}} \cr & \Rightarrow {\text{Remaining Distance}} \cr & = 1 - \left( {\frac{1}{3} + \frac{1}{4}} \right) \cr & = \frac{5}{{12}}{\text{ km}} \cr & \therefore {\text{Average speed}} \cr & = \frac{1}{{\frac{1}{{3 \times 80}} + \frac{1}{{50 \times 4}} + \frac{{1 \times 5}}{{100 \times 12}}}} \cr & = \frac{1}{{\frac{{5 + 6 + 5}}{{1200}}}} \cr & = \frac{{1200}}{6} \cr & = 75{\text{ km/hr}} \cr} $$