Answer to Question #145078 in Physics for buddy

Question

A construction worker drives to his work 43 km away at an average speed of 62 km/h. Before he gets out of his car he realizes he forgot his hammer at home and drives back at 79 km/h. Assuming his time parked at work was insignificant, what was his average speed overall in km/h?

Answer 1

By defintion, the average speed is:

$$v = \dfrac{total\space distance}{total\space time}$$

The total distance is:

$$total \space distance =43km+43km = 86km$$

The time spent for the way to work is:

$$\dfrac{43km}{62km/h} = \dfrac{43}{62}h$$

The time spent for the way to home is:

$$\dfrac{43km}{79km/h} = \dfrac{43}{79}h$$

Thus, the total time is:

$$total\space time = \dfrac{43}{62}h + \dfrac{43}{79}h = \dfrac{6063}{4898}h$$

And the average speed is:

$$v = \dfrac{86km}{\dfrac{6063}{4898}h} \approx 69.5\space km/h$$

Answer. $69.5\space km/h$.