A motorist average 48km/h for the first 30km of a journey and 64km/h for the next 120km.what is the average speed for the whole journey

Answer 1

To determine the average speed for the entire journey, we need to first find the total distance traveled and the total time taken for the journey.

1. **Calculate total distance:**

The total distance is the sum of the distances for both segments of the journey:
\[ \text{Total distance} = 30 \, \text{km} + 120 \, \text{km} = 150 \, \text{km} \]

2. **Calculate time taken for each segment:**

- For the first segment:
\[ \text{Time}_{\text{first segment}} = \frac{\text{Distance}_{\text{first segment}}}{\text{Speed}_{\text{first segment}}} = \frac{30 \, \text{km}}{48 \, \text{km/h}} = \frac{30}{48} \, \text{hours} = \frac{5}{8} \, \text{hours} = 0.625 \, \text{hours} \]

- For the second segment:
\[ \text{Time}_{\text{second segment}} = \frac{\text{Distance}_{\text{second segment}}}{\text{Speed}_{\text{second segment}}} = \frac{120 \, \text{km}}{64 \, \text{km/h}} = \frac{120}{64} \, \text{hours} = \frac{15}{8} \, \text{hours} = 1.875 \, \text{hours} \]

3. **Calculate total time:**

\[ \text{Total time} = \text{Time}_{\text{first segment}} + \text{Time}_{\text{second segment}} = 0.625 \, \text{hours} + 1.875 \, \text{hours} = 2.5 \, \text{hours} \]

4. **Calculate the average speed:**

The average speed for the whole journey is the total distance divided by the total time:
\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{150 \, \text{km}}{2.5 \, \text{hours}} = 60 \, \text{km/h} \]

So, the average speed for the whole journey is \( 60 \, \text{km/h} \).