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=(d_1)/(s_1)`

The expression for the final time taken is given as:

`t_2=(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)=(d_1+d_2)/(t_1+t_2) \\ S_(Avg)=\frac{d_1+d_2}{(d_1)/(s_1)+(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.