Question

Sally travels by car from one city to another. She drives for 29.0 min at 52.0 km/h, 31.0 min at 30.0 km/h, and 27.0 min at 56.0 km/h, and she spends 10.0 min eating lunch and buying gas.

Answer 1

Answer on Question #48145, Physics, Other

Sally travels by car from one city to another. She drives for 29.0 min at $52.0 \, \text{km/h}$, 31.0 min at 30.0 km/h, and 27.0 min at 56.0 km/h, and she spends 10.0 min eating lunch and buying gas.

By the definition, average speed is:

$$v_{av} = \frac{S_{total}}{t_{total}}$$

To find time in hours:

$$t_h = \frac{t_{min}}{60}$$

Traveled distance:

$$S = vt$$

So, average speed is:

$$\begin{aligned} v_{av} &= \frac{v_1 \frac{t_1}{60} + v_2 \frac{t_2}{60} + v_2 \frac{t_3}{60}}{\frac{t_1}{60} + \frac{t_2}{60} + \frac{t_3}{60} + \frac{t_4}{60}} = \frac{v_1 t_1 + v_2 t_2 + v_2 t_3}{t_1 + t_2 + t_3 + t_4} \\ v_{av} &= \frac{52.0 \, \frac{\text{km}}{\text{h}} \cdot 29.0 \, \text{min} + 30.0 \, \frac{\text{km}}{\text{h}} \cdot 31.0 \, \text{min} + 56.0 \, \frac{\text{km}}{\text{h}} \cdot 27.0 \, \text{min}}{29.0 \, \text{min} + 31.0 \, \text{min} + 27.0 \, \text{min} + 10.0 \, \text{min}} \approx 40.7 \, \frac{\text{km}}{\text{h}} \end{aligned}$$

Answer: Average speed: $v_{av} \approx 40.7 \, \frac{\text{km}}{\text{h}}$

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