Mr. Y travelled 438 km, 820 km and 972 km at a speed of 6 km/hr, 20 km/hr and 27 km/hr, respectively. Find his average speed in km/hr.

The correct option is:
$$14\frac{13}{15}$$

Step-by-Step Explanation:

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

Step 1: Calculate the total distance travelled
Mr. Y travels three different distances: 438 km, 820 km, and 972 km.
$$\text{Total Distance}=438+820+972=2230\text{km}$$

Step 2: Calculate the time taken for each part of the journey
Time taken for each interval is calculated as:
$$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$$

Let t₁, t₂, and t₃ be the times taken for the first, second, and third parts of the journey respectively:
For the first part (438 km at 6 km/hr):
$$t_1=\frac{438}{6}=73\text{hours}$$
For the second part (820 km at 20 km/hr):
$$t_2=\frac{820}{20}=41\text{hours}$$
For the third part (972 km at 27 km/hr):
$$t_3=\frac{972}{27}=36\text{hours}$$

Step 3: Calculate the total time taken
$$\text{Total Time}=73+41+36=150\text{hours}$$

Step 4: Calculate the average speed
Substitute the total distance and total time into our average speed formula:
$$\text{Average Speed}=\frac{2230}{150}$$
Simplifying the fraction by dividing the numerator and denominator by 10:
$$\text{Average Speed}=\frac{223}{15}\text{km/hr}$$

Step 5: Convert to a mixed fraction
Dividing 223 by 15:
223 ÷ 15 = 14 with a remainder of 13.
Thus, we can write the result as:
$$14\frac{13}{15}\text{km/hr}$$