Amit travels 30 minutes at the speed of 25 km/hr. Further he travels 20 minutes at the speed of 40 km/hr. Find his average speed.

Options

A. 25 km/hr
B. 30 km/hr
C. 31 km/hr
D. none of these

Answer

To find Amit's average speed, we will follow these steps:

### Step 1: Calculate the distance traveled during the first part of the journey.
Amit travels for 30 minutes at a speed of 25 km/hr.

- Convert 30 minutes to hours:
\[ 30 \text{ minutes} = \frac{30}{60} = 0.5 \text{ hours} \]

- Use the formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 25 \text{ km/hr} \times 0.5 \text{ hr} = 12.5 \text{ km} \]

### Step 2: Calculate the distance traveled during the second part of the journey.
Amit travels for 20 minutes at a speed of 40 km/hr.

- Convert 20 minutes to hours:
\[ 20 \text{ minutes} = \frac{20}{60} = \frac{1}{3} \text{ hours} \]

- Use the formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 40 \text{ km/hr} \times \frac{1}{3} \text{ hr} = \frac{40}{3} \text{ km} \approx 13.33 \text{ km} \]

### Step 3: Calculate the total distance traveled.
Now, we add the distances from both parts of the journey:
\[ \text{Total Distance} = 12.5 \text{ km} + \frac{40}{3} \text{ km} \]

To add these, convert 12.5 km to a fraction:
\[ 12.5 = \frac{25}{2} \text{ km} \]

Now we find a common denominator (which is 6):
\[ \frac{25}{2} = \frac{75}{6} \text{ km} \]
\[ \frac{40}{3} = \frac{80}{6} \text{ km} \]

Now add them:
\[ \text{Total Distance} = \frac{75}{6} + \frac{80}{6} = \frac{155}{6} \text{ km} \]

### Step 4: Calculate the total time taken.
Total time is the sum of the time taken for both parts of the journey:
\[ \text{Total Time} = 30 \text{ minutes} + 20 \text{ minutes} = 50 \text{ minutes} \]

Convert 50 minutes to hours:
\[ 50 \text{ minutes} = \frac{50}{60} = \frac{5}{6} \text{ hours} \]

### Step 5: Calculate the average speed.
Average speed is given by the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{\frac{155}{6} \text{ km}}{\frac{5}{6} \text{ hr}} \]

When dividing fractions, multiply by the reciprocal:
\[ \text{Average Speed} = \frac{155}{6} \times \frac{6}{5} = \frac{155}{5} = 31 \text{ km/hr} \]

### Conclusion
Amit's average speed is **31 km/hr**.

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