Question

A man travels 1st 50 km at 25 km/hr, next 40 km with 20 km/hr and then 90 km at 15 km/hr. Find his average speed for the whole journey (in km/hr).

Answer 1

Hint: We will first find the total distance travelled by the man and then find the total time taken by him to cover that distance. And finally we will find the average speed of the man for the entire journey by using the formula of average speed, which is, $\dfrac{\text{total distance covered}}{\text{total time taken}}$.

Complete step-by-step solution -
It is given in the question that a man travels 1st 50 km at 25 km/hour, next 40 km with 20 km/hour and then 90 km at 15 km/hr. Find his average speed for the whole journey (in km/hr). We have to find the average speed of the man for the entire journey. To find this, we have to find the total distance covered by the man and also the time taken by him to cover that distance.
So, the total distance covered by the man will be $=50km+40km+90km=180km$.
The total time taken by the man will be ${{t}_{1}}+{{t}_{2}}+{{t}_{3}}$. Now, we know that $\text{time}=\dfrac{\text{distance}}{\text{speed}}$.
So, ${{t}_{1}}$ can be calculated as, $\dfrac{\text{distance travelled in first interval}}{\text{speed of man in first interval}}=\dfrac{50km}{25km/hr}=2hrs$. So, ${{t}_{1}}$ is $2hrs$.
${{t}_{2}}$ can be calculated as, $\dfrac{\text{distance travelled in second interval}}{\text{speed of man in second interval}}=\dfrac{40km}{20km/hr}=2hrs$. So, ${{t}_{2}}$ is $2hrs$.
${{t}_{3}}$ can be calculated as, $\dfrac{\text{distance travelled in third interval}}{\text{speed of man in third interval}}=\dfrac{90km}{15km/hr}=6hrs$. So, ${{t}_{3}}$ is $6hrs$.
So, the total time taken is $={{t}_{1}}+{{t}_{2}}+{{t}_{3}}=2hrs+2hrs+6hrs=10hrs$.
Now, the average speed of the man for the entire journey will be,$=\dfrac{\text{total distance travelled}}{\text{total time taken}}=\dfrac{180km}{10hrs}=18km/hr$.
Therefore, the average speed for the man for the whole journey will be $18km/hr$.

Note: In this question, there is a possibility that many students consider the total distance as $=50km+40km+90km=180km$ and the total time as $=\dfrac{180}{25+20+15}=3hrs$, which leads to the wrong answer, where we get the average speed of the man as $60km/hr$. They forget to use the formula for calculating time, which is, $=\dfrac{\text{distance}}{\text{speed}}$. So, it is recommended to solve this question step by step to reach the correct answer.