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

Options

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

Explanation

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

### Step 1: Convert Time from Minutes to Hours
Amit travels for two different durations: 30 minutes and 20 minutes. We need to convert these times into hours since the speed is given in km/hr.

- **30 minutes** = 30/60 = 0.5 hours
- **20 minutes** = 20/60 = 1/3 hours (or approximately 0.333 hours)

### Step 2: Calculate the Distance for Each Segment
Using the formula for distance, which is Distance = Speed × Time, we can calculate the distance for each segment of the journey.

1. **First Segment:**
- Speed = 25 km/hr
- Time = 0.5 hours
- Distance = 25 km/hr × 0.5 hours = 12.5 km

2. **Second Segment:**
- Speed = 40 km/hr
- Time = 1/3 hours
- Distance = 40 km/hr × (1/3) hours = 40/3 km ≈ 13.33 km

### Step 3: Calculate Total Distance
Now, we will add the distances from both segments to find the total distance traveled.

- Total Distance = Distance from First Segment + Distance from Second Segment
- Total Distance = 12.5 km + 13.33 km = 25.83 km

### Step 4: Calculate Total Time
Next, we will add the time taken for both segments to find the total time.

- Total Time = Time from First Segment + Time from Second Segment
- Total Time = 0.5 hours + (1/3) hours
- To add these, we convert 0.5 to a fraction: 0.5 = 3/6
- Total Time = 3/6 + 2/6 = 5/6 hours

### Step 5: Calculate Average Speed
Finally, we can find the average speed using the formula:

- Average Speed = Total Distance / Total Time
- Average Speed = 25.83 km / (5/6) hours
- To divide by a fraction, we multiply by its reciprocal:
- Average Speed = 25.83 km × (6/5) = 31.0 km/hr

### Solution
Amit's average speed during his journey is approximately **31.0 km/hr**.

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