Question

John should drive to his workplace and back home.

On the way to the workplace it was raining, so he drove at speed of $42mph$.

On the way back the rain was over so his speed was $54mph$.

What was John's average speed, for the whole trip?

Answer 1

Explanation to correct Answer:

Step-1:Finding the total distance and total time:

Given,

Let the distance between the workplace and home be $d$

Speed of the vehicle home to workplace =$42mph$

Speed of the vehicle workplace to home=$54mph$

Time is taken while raining

$=\frac{d}{42}$ [We know that $\text{time}=\frac{\text{distance}}{\text{speed}}$]

Time is taken while not raining

$=\frac{d}{54}$

Total distance= workplace to home+ home to workplace

$$\begin{gathered} =d+d \\ =2d \end{gathered}$$

Total time $=$ Speed of the vehicle home to workplace $+$ Speed of the vehicle workplace to home

$$\begin{gathered} =\frac{d}{42}+\frac{d}{54} \\ =\frac{d\left(42+54\right)}{42\times 54} \\ =\frac{96d}{2268} \end{gathered}$$

Step-2: Finding the average speed:

$$\begin{gathered} \text{Average speed}=\frac{\text{Total distance}}{\text{Total}\mathrm{time}} \\ =\frac{2d}{{\displaystyle \frac{96d}{2268}}} \\ =\frac{2268\times 2}{96} \\ =47.25 \end{gathered}$$

Hence, the average speed for the whole trip is $47.25mph$.