Mary jogs 9 km at a speed of 6 km per hour. At what speed would she need to jog during the next 1.5 hours to have an average of 9 km per hour for the entire jogging session ?

Let speed of jogging be x km/hr
Total time taken :
$$\eqalign{ & = \left( {\frac{9}{6}{\text{hrs}} + 1.5{\text{ hrs}}} \right) \cr & = 3{\text{ hrs}} \cr} $$
Total distance covered = $$\left( {9 + 1.5x} \right){\text{ km}}$$
$$\eqalign{ & \therefore \frac{{9 + 1.5x}}{3} = 9 \cr & \Leftrightarrow 9 + 1.5x = 27 \cr & \Leftrightarrow \frac{3}{2}x = 18 \cr & \Leftrightarrow x = \left( {18 \times \frac{2}{3}} \right) \cr & \Leftrightarrow x = 12{\text{ kmph}} \cr} $$