Mr. W travelled 425 km, 946 km and 340 km at a speed of 5 km/hr, 43 km/hr and 34 km/hr, respectively. Find his average speed in km/hr.

The correct option is:
$14\frac{73}{117}$

Step-by-Step Explanation:

To find the average speed of Mr. W throughout his journey, we use the standard formula:
$\text{Average Speed}=\frac{\text{Total Distance}}{\text{Total Time}}$

Step 1: Calculate the total distance travelled
Mr. W travelled three distinct intervals: 425 km, 946 km, and 340 km.
$\text{Total Distance}=425+946+340=1711\text{km}$

Step 2: Calculate the time taken for each part of the journey
The time taken for each interval is calculated as:
$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$
Let's find the time for each of the three parts:
1. Time taken for the first part:
$t_1=\frac{425}{5}=85\text{hours}$
2. Time taken for the second part:
$t_2=\frac{946}{43}=22\text{hours}$
3. Time taken for the third part:
$t_3=\frac{340}{34}=10\text{hours}$

Step 3: Calculate the total time taken
Sum the times taken for all parts of the journey:
$\text{Total Time}=85+22+10=117\text{hours}$

Step 4: Calculate the average speed
Divide the total distance by the total time:
$\text{Average Speed}=\frac{1711}{117}\text{km/hr}$
To express this improper fraction as a mixed fraction, we divide 1711 by 117:
$1711=(117\times 14)+73$
This gives:
$\text{Average Speed}=14\frac{73}{117}\text{km/hr}$