Question

A man covers half of his journey at 6km/hr and the remaining half at 3km/hr. His average speed is
a) 3km/hr
b) 4km/hr
c) 4.5km/hr
d) 9km/hr

Answer 1

Hint: We know the formula to calculate the time if speed and distance covered is given. We will first calculate the time taken by the man to cover the first half of the distance. We will calculate the time taken by the man for the second half of the distance. We know that $Average\text{ }Speed= \dfrac{total\text{ }dist.}{total\ time\text{ }taken}$ .

Complete step by step answer:
Let the total distance travelled by the man = 2d
We know that the man covers half of his journey at 6km/hr.
Let the time taken for the first half be t1
$\begin{align}
  & \Rightarrow \text{time}= \dfrac{\text{distance}}{\text{speed}} \\
 & \Rightarrow {{t}_{1}}= \dfrac{d}{6} \\
\end{align}$
We know that the man covers the remaining half of his journey at 3km/hr.
Let the time taken for the remaining half be t2
$\begin{align}
  & \Rightarrow \text{time}= \dfrac{\text{distance}}{\text{speed}} \\
 & \Rightarrow {{t}_{2}}= \dfrac{d}{3} \\
\end{align}$
We know that $Average\text{ }Speed= \dfrac{total\text{ }dist.}{total\ time\text{ }taken}$ .
Total distance =2d
Total time taken= t1+t2
$\begin{align}
  & \Rightarrow \dfrac{d}{6}+ \dfrac{d}{3} \\
 & \Rightarrow {{t}_{1}}+{{t}_{2}}= \dfrac{\left( d+2d \right)}{6} \\
 & \Rightarrow {{t}_{1}}+{{t}_{2}}= \dfrac{d}{2} \\
\end{align}$
We will now put the value in formula, we will get
$\Rightarrow Average\text{ }Speed= \dfrac{2d}{ \dfrac{d}{2}}$
We will solve the above equation and we will get,
Average Speed = 4km/hr

Note:
As we know that the speed at which the man travels is not constant so the time taken to cover each half will not be the same. Many students just add both the speeds and then divide it by 2 this will give the wrong answer. Avoid making these mistakes.