A man, on tour, travels first 160 km at 64 km/h and the next 160 km at 80 km/h. The average speed for the first 320 km of the tour is

Options

A. 71 km/h
B. 71.11 km/h
C. 72 km/h
D. 71.12 km/h

Answer

To find the average speed for the first 320 km of the tour, we will follow these steps:

### Step 1: Calculate the time taken for the first part of the journey.
The first part of the journey is 160 km at a speed of 64 km/h.

**Formula for time:**
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

**Calculation:**
\[ T_1 = \frac{160 \text{ km}}{64 \text{ km/h}} = 2.5 \text{ hours} \]

### Step 2: Calculate the time taken for the second part of the journey.
The second part of the journey is also 160 km, but at a speed of 80 km/h.

**Calculation:**
\[ T_2 = \frac{160 \text{ km}}{80 \text{ km/h}} = 2 \text{ hours} \]

### Step 3: Calculate the total distance and total time.
The total distance traveled is:
\[ \text{Total Distance} = 160 \text{ km} + 160 \text{ km} = 320 \text{ km} \]

The total time taken is:
\[ \text{Total Time} = T_1 + T_2 = 2.5 \text{ hours} + 2 \text{ hours} = 4.5 \text{ hours} \]

### Step 4: Calculate the average speed.
The average speed is given by the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

**Calculation:**
\[ \text{Average Speed} = \frac{320 \text{ km}}{4.5 \text{ hours}} = \frac{320}{4.5} \approx 71.11 \text{ km/h} \]

### Final Answer:
The average speed for the first 320 km of the tour is approximately **71.11 km/h**.

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