Question

A train has a speed of $60$ km/hr for the first one hour and $40$ km/hr for the next half hour. Its average speed in km/hr is

• A. $50$
• B. $53.33$
• C. $48$
• D. $70$

Answer 1

The correct option is B

$53.33$

Explanation for the correct option:

Step 1: Find the distance travelled by the train in first hour:

Given, The speed of the train in first $1$ hour is $60$ km/hr.

Hence distance travelled by the train in the first $1$ hour is

$\begin{array}{rcl}\mathit{D}\mathit{i}\mathit{s}\mathit{t}\mathit{a}\mathit{n}\mathit{c}\mathit{e}& \mathbf{=}& \mathit{s}\mathit{p}\mathit{e}\mathit{e}\mathit{d}\mathbf{\times }\mathit{t}\mathit{i}\mathit{m}\mathit{e}\\ & =& 60\times 1\\ & =& 60km\end{array}$

Step 2. Find the distance travelled by the train in next half hour:

Given, Speed of the train for next half hour is $40$ km/hr.

Hence distance travelled by the train in the next half hour is

$\begin{array}{rcl}\mathit{D}\mathit{i}\mathit{s}\mathit{t}\mathit{a}\mathit{n}\mathit{c}\mathit{e}& \mathbf{=}& \mathit{s}\mathit{p}\mathit{e}\mathit{e}\mathit{d}\mathbf{\times }\mathit{t}\mathit{i}\mathit{m}\mathit{e}\\ & =& 40\times \frac{1}{2}\\ & =& 20km\end{array}$

Step 3. Find the average speed of train

Average Speed$=\frac{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{d}\mathbf{i}\mathbf{s}\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{c}\mathbf{e}}{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{t}\mathbf{i}\mathbf{m}\mathbf{e}}$

$\begin{array}{rcl}& =& \frac{\left(60+20\right)}{\left(1+{\displaystyle \frac{1}{2}}\right)}\\ & =& \frac{80}{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}\\ & =& \mathbf{53}\mathbf{.}\mathbf{33}\mathbf{}\mathit{k}\mathit{m}\mathbf{/}\mathit{h}\mathit{r}\end{array}$

Hence, option B is correct.