A man travel from A to B at a speed of 29 km/hr in 29 min. and he travel a distance from B to C with a speed of 39 km/hr in 29 min. Find the average speed of whole journey.

Options

A. 43 km/hr
B. 34 km/hr
C. 39 km/hr
D. 40 km/hr

Answer

To find the average speed of the whole journey from A to C, we need to follow these steps:

### Step 1: Calculate the distance from A to B
The speed from A to B is given as 29 km/hr, and the time taken is 29 minutes. First, we need to convert the time from minutes to hours.

\[ \text{Time in hours} = \frac{29 \text{ minutes}}{60} = \frac{29}{60} \text{ hours} \]

Now, we can calculate the distance using the formula:

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

\[ \text{Distance from A to B} = 29 \text{ km/hr} \times \frac{29}{60} \text{ hr} = \frac{29 \times 29}{60} \text{ km} = \frac{841}{60} \text{ km} \]

### Step 2: Calculate the distance from B to C
The speed from B to C is given as 39 km/hr, and the time taken is also 29 minutes. We will convert the time from minutes to hours in the same way.

\[ \text{Time in hours} = \frac{29 \text{ minutes}}{60} = \frac{29}{60} \text{ hours} \]

Now, we can calculate the distance:

\[ \text{Distance from B to C} = 39 \text{ km/hr} \times \frac{29}{60} \text{ hr} = \frac{39 \times 29}{60} \text{ km} = \frac{1131}{60} \text{ km} \]

### Step 3: Calculate the total distance
Now, we can find the total distance traveled from A to C:

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

\[ \text{Total Distance} = \frac{841}{60} + \frac{1131}{60} = \frac{841 + 1131}{60} = \frac{1972}{60} \text{ km} \]

### Step 4: Calculate the total time
The total time taken for the journey is the sum of the time taken for each segment:

\[ \text{Total Time} = \frac{29}{60} + \frac{29}{60} = \frac{29 + 29}{60} = \frac{58}{60} \text{ hours} \]

### Step 5: Calculate the average speed
Finally, we can calculate the average speed using the formula:

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

\[ \text{Average Speed} = \frac{\frac{1972}{60}}{\frac{58}{60}} = \frac{1972}{58} \text{ km/hr} \]

Calculating this gives:

\[ \text{Average Speed} = 34 \text{ km/hr} \]

### Final Answer
The average speed of the whole journey is **34 km/hr**.

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