Understanding Average Speed Calculation for a Journey

This problem involves calculating the average speed for a journey that consists of multiple parts, each with a different distance and speed. The key to solving this is understanding the fundamental formula for average speed:

Average Speed = Total Distance / Total Time

We need to find the total distance traveled and the total time taken for the entire journey.

Step 1: Calculate the Total Distance

Rishi travels in three segments. To find the total distance, we simply add the distances of each segment:

Total Distance = Distance_1 + Distance_2 + Distance_3

Total Distance = $198 \text{ km} + 584 \text{ km} + 656 \text{ km}$

Total Distance = $1438 \text{ km}$

Step 2: Calculate the Time Taken for Each Segment

The formula relating distance, speed, and time is: Time = Distance / Speed. We will use this for each part of Rishi's journey.

Segment 1:

Distance_1 = $198 \text{ km}$

Speed_1 = $66 \text{ km/hr}$

Time_1 = $\frac{\text{Distance}_1}{\text{Speed}_1} = \frac{198 \text{ km}}{66 \text{ km/hr}} = 3 \text{ hr}$

Segment 2:

Distance_2 = $584 \text{ km}$

Speed_2 = $73 \text{ km/hr}$

Time_2 = $\frac{\text{Distance}_2}{\text{Speed}_2} = \frac{584 \text{ km}}{73 \text{ km/hr}} = 8 \text{ hr}$

Segment 3:

Distance_3 = $656 \text{ km}$

Speed_3 = $82 \text{ km/hr}$

Time_3 = $\frac{\text{Distance}_3}{\text{Speed}_3} = \frac{656 \text{ km}}{82 \text{ km/hr}} = 8 \text{ hr}$

Step 3: Calculate the Total Time

Now, we add the time taken for each segment to get the total time for the journey:

Total Time = Time_1 + Time_2 + Time_3

Total Time = $3 \text{ hr} + 8 \text{ hr} + 8 \text{ hr}$

Total Time = $19 \text{ hr}$

Step 4: Calculate the Average Speed

Using the formula for average speed with the total distance and total time calculated:

Average Speed = $\frac{\text{Total Distance}}{\text{Total Time}}$

Average Speed = $\frac{1438 \text{ km}}{19 \text{ hr}}$

Average Speed $\approx 75.68421 \text{ km/hr}$

Step 5: Round the Answer

The question asks to round the answer to two decimal places. Rounding $75.68421$ to two decimal places gives us $75.68$.

Therefore, Rishi's average speed for the whole journey is approximately 75.68 km/hr.