If you travel to work at an average speed of 3 m/s and return home at an average speed of 9 m/s what is the average speed for the whole journey...

Let the distance to work be d. The time to go to work becomes:

Time_1 = \frac{x}{3}

The time to come from work is given by:

Time_2 = \frac{x}{9}

Average speed is given by the total distance divided by the total time.

Average\ Speed = \Large{\frac{x + x}{ \frac{x}{3}+ \frac{x}{9}}}