Question

You drive 5 miles at 30 mi/hr and then another 3 miles at 50 mi/hr. What is your average speed for the whole8-mile trip?

Answer 1

Given data

The initial distance covered is d1 = 5 miles

The initial speed is s1 = 30 mi/hr

The final distance is d2 = 3 miles

The final speed is s2 = 50 mi/hr

The expression for the initial time taken to travel is given as:

$t_1=\frac{d_1}{s_1}$

The expression for the final time taken is given as:

$t_2=\frac{d_2}{s_2}$

The expression for the average speed for the whole trip is given as:

$\begin{gathered} \text{Average sp}eed\text{ =}\frac{total\text{ distance}}{total\text{ time}} \\ S_{Avg}=\frac{d_1+d_2}{t_1+t_2} \\ S_{Avg}=\frac{d_1+d_2}{\frac{d_1}{s_1}+\frac{d_2}{s_2}_{}} \end{gathered}$

Substitute the value in the above equation.

$\begin{gathered} S_{Avg}=\frac{5\text{ mi+3 mi}}{\frac{5\text{ mi}}{30\text{ mi/hr}}+\frac{3\text{ mi}}{50\text{ mi/hr}}} \\ S_{Avg}=35.3\text{ mi/hr} \end{gathered}$

Thus, the average speed for the whole trip is 35.3 mi/hr.