Question

You jog at 9.5km/hr for 8.0km, then you jump into a car and drive an additional 16km. With what average speed must you drive your car if your average speed for the entire 24km is to be 22km/hr?
The answer is 64km/hr, but I can't figure out how to get it

Answer 1

Average speed is the total distance/total time consumed.
Solve the following for R. the average speed to meet the problem requirements:\[\frac{24\text{ km}}{\frac{8.0\text{ km}}{9.5\text{ km}/\text{hr}}+\frac{16\text{ km}}{R \text{ km}/\text{hr}}}=22\text{ km}/\text{hr}\]R =64.3077 km/hr

From Mathematica:\[\text{Solve}\left[\frac{24}{\frac{8.0}{9.5}+\frac{16}{r}}= 22,r\right]\]\[\{\{r\to 64.3077\}\} \]