Average Speed Calculation Steps

To determine the average speed for the entire journey, we need to calculate the total distance traveled and divide it by the total time spent traveling.

Part 1: Initial Driving Phase

• Speed (\(v_1\)): \(59\) kmph
• Time (\(t_1\)): \(3.5\) hours
• Distance covered (\(d_1\)): Calculated as Speed × Time. \( d_1 = v_1 \times t_1 \) \( d_1 = 59 \text{ kmph} \times 3.5 \text{ hours} = 206.5 \text{ km} \)

Part 2: Increased Speed Phase

• Speed increase: \(9\) kmph
• New Speed (\(v_2\)): The speed increased from the initial speed. \( v_2 = v_1 + 9 \text{ kmph} \) \( v_2 = 59 \text{ kmph} + 9 \text{ kmph} = 68 \text{ kmph} \)
• Time (\(t_2\)): \(1\) hour
• Distance covered (\(d_2\)): Calculated as New Speed × Time. \( d_2 = v_2 \times t_2 \) \( d_2 = 68 \text{ kmph} \times 1 \text{ hour} = 68 \text{ km} \)

Total Journey Summary

• Total Distance (\(D\)): Sum of distances from both parts. \( D = d_1 + d_2 \) \( D = 206.5 \text{ km} + 68 \text{ km} = 274.5 \text{ km} \)
• Total Time (\(T\)): Sum of times from both parts. \( T = t_1 + t_2 \) \( T = 3.5 \text{ hours} + 1 \text{ hour} = 4.5 \text{ hours} \)

Final Average Speed Calculation

The average speed (\(v_{avg}\)) is the total distance divided by the total time.

\( v_{avg} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{D}{T} \)

Substituting the calculated values:

\( v_{avg} = \frac{274.5 \text{ km}}{4.5 \text{ hours}} \)

\( v_{avg} = 61 \text{ kmph} \)