Chapter 1, Problem 15P

To determine

To find: The average speed during the whole trip.

Answer to Problem 15P

Solution:

The average speed is 40 mi/h.

Explanation of Solution

Given:

Speed during the first half distance = 30 mi/h

Speed during the second half distance = 60 min/h

Result used:

$\text{Average speed}=\frac{\text{Total distance}}{\text{Total time}}$

Calculation:

Let $t_1$ be the time taken for the first half.

Let $t_2$ be the time taken for the second half.

Distance traveled on each half on the trip is d

Therefore, the total distance is 2d.

From the given data the time taken for the first half trip is $t_1=\frac{d}{30}$.

Time taken for the second half trip is $t_2=\frac{d}{60}$.

$\begin{array}{c}\text{Average speed}=\frac{2d}{t_1+t_2}\\ =\frac{2d}{\frac{d}{30}+\frac{d}{60}}\\ =\frac{2d}{\frac{3d}{60}}\\ =40\end{array}$

Thus, the average speed is 40 mi/h.