A car travels from A to B and then C. The car takes 3 h to travel from A to B at an average speed of 42 km/h .It travels 128 km from B to C at an average speed of 64 km/h . If the car takes a total of 5 h , what is the average speed of the car travelling from A to C ?

Options

A. 55 km/h
B. 22 km/h
C. `50.8` km/h
D. 53 km/h

Answer

To solve the problem, we need to find the average speed of the car traveling from A to C. We will break down the solution step by step.

### Step 1: Calculate the distance from A to B
The car takes 3 hours to travel from A to B at an average speed of 42 km/h. We can use the formula:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Substituting the values:

\[ \text{Distance from A to B} = 42 \, \text{km/h} \times 3 \, \text{h} = 126 \, \text{km} \]

### Step 2: Calculate the time taken to travel from B to C
The car travels 128 km from B to C at an average speed of 64 km/h. We can again use the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the values:

\[ \text{Time from B to C} = \frac{128 \, \text{km}}{64 \, \text{km/h}} = 2 \, \text{h} \]

### Step 3: Calculate the total time taken
The total time taken for the journey from A to C is given as 5 hours. We can find the time taken from A to C by adding the time taken from A to B and B to C:

\[ \text{Total time} = \text{Time from A to B} + \text{Time from B to C} \]

Substituting the known values:

\[ 5 \, \text{h} = 3 \, \text{h} + \text{Time from B to C} \]

From this, we can confirm that:

\[ \text{Time from B to C} = 2 \, \text{h} \]

### Step 4: Calculate the total distance from A to C
Now we can find the total distance traveled from A to C by adding the distances from A to B and B to C:

\[ \text{Total distance from A to C} = \text{Distance from A to B} + \text{Distance from B to C} \]

Substituting the values:

\[ \text{Total distance from A to C} = 126 \, \text{km} + 128 \, \text{km} = 254 \, \text{km} \]

### Step 5: Calculate the average speed from A to C
Finally, we can calculate the average speed of the car traveling from A to C using the formula:

\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

Substituting the values:

\[ \text{Average Speed} = \frac{254 \, \text{km}}{5 \, \text{h}} = 50.8 \, \text{km/h} \]

### Final Answer
The average speed of the car traveling from A to C is **50.8 km/h**.