Question

You drive 4 km at 30 km/h and then another 4 km at 50 km/h. What is your average speed for the whole 8-km trip?

(a) More than 40 km/h.

(b) Equal to 40 km/h

(c) Less than 40 km/h

(d) Not enough information.

Short answer

The correct option is (c) Less than $40\mathrm{km}/\mathrm{h}$.

Step-by-step solution

Step 1. Definition of the average speed of the trip

It establishes a relationship between the total distance and the time taken in the trip. Total distance is the sum of all distance values, and total time is the sum of the time values.

Step 2. Formula for average speed

The expression for average speed is:

$s_{avg}=\frac{∆d}{∆t}$

Here, $∆d$ is the total distance and$∆t$ is the total time taken.

Step 3. Determination of time using distance as 4 km and speed as 30 km/h

The time taken in the first trip can be calculated as:

$\begin{array}{rcl}\mathrm{Time}& =& \frac{\mathrm{Distance}}{\mathrm{Speed}}\\ t_1& =& \frac{d_1}{s_1}\end{array}$

Substitute the values as 4 km for $d_1$and 30 km/h for $s_1$.

$\begin{array}{rcl}{t}_1& =& \frac{4\mathrm{km}}{30\mathrm{km}/\mathrm{h}}\\ & =& 0.133\mathrm{h}\end{array}$

Step 4. Determination of time using distance as 4 km speed as 50 km/h

The time taken in the second trip can be calculated as:

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

Substitute the values as 4 km for $d_2$and 50 km/h for $s_2$.

role="math" localid="1642658518499" $\begin{array}{rcl}{t}_2& =& \frac{4\mathrm{km}}{50\mathrm{km}/\mathrm{h}}\\ & =& 0.08\mathrm{h}\end{array}$

Step 5. Determination of the total time taken

The total time taken in the whole trip can be calculated as:

$∆t=t_1+t_2$

Substitute the values as 0.133 h for $t_1$and 0.08 h for $t_2$.

role="math" localid="1642659024437" $\begin{array}{rcl}∆t& =& 0.133\mathrm{h}+0.08\mathrm{h}\\ & =& 0.213\mathrm{h}\end{array}$

Step 6. Determination of the total distance covered

The total distance covered in the whole trip can be calculated as:

$∆d=d_1+d_2$

Substitute the values as 4 km for $d_1$and 4 km for $d_2$.

$\begin{array}{rcl}∆d& =& 4\mathrm{km}+4\mathrm{km}\\ & =& 8\mathrm{km}\end{array}$

Step 7. Determination of the average speed

The average speed for the whole trip can be calculated as:

$s_{avg}=\frac{∆d}{∆t}$

Substitute the values as 8 km for$∆d$ and 0.213 h for $∆t$.

$\begin{array}{rcl}{s}_{avg}& =& \frac{8\mathrm{km}}{0.213\mathrm{h}}\\ & =& 37.559\mathrm{km}/\mathrm{h}\end{array}$

The average speed is $37.559\mathrm{km}/\mathrm{h}$, which is less than 40 km/h.

Hence, the correct option is (c).