A person covers 9 km with a speed of 3 km/h, 25 km with a speed of 5 km/h and 30 km with a speed of 10 km/h. Find out the average speed of person.

Options

A. `5(9)/(11)`
B. `11 (5)/(9) km//h`
C. `9 (5)/(11) km//h`
D. `5 (5)/(11) km//h`

Answer

To find the average speed of the person, we will follow these steps:

### Step 1: Calculate Total Distance
First, we need to find the total distance covered by the person. The distances covered are:
- 9 km
- 25 km
- 30 km

**Total Distance = 9 km + 25 km + 30 km**

**Calculation:**
Total Distance = 9 + 25 + 30 = 64 km

### Step 2: Calculate Total Time
Next, we need to calculate the total time taken to cover each distance. We will use the formula:

**Time = Distance / Speed**

1. For the first part (9 km at 3 km/h):
**Time = 9 km / 3 km/h = 3 hours**

2. For the second part (25 km at 5 km/h):
**Time = 25 km / 5 km/h = 5 hours**

3. For the third part (30 km at 10 km/h):
**Time = 30 km / 10 km/h = 3 hours**

Now, we can calculate the total time taken:

**Total Time = 3 hours + 5 hours + 3 hours**

**Calculation:**
Total Time = 3 + 5 + 3 = 11 hours

### Step 3: Calculate Average Speed
Now that we have both the total distance and total time, we can find the average speed using the formula:

**Average Speed = Total Distance / Total Time**

**Calculation:**
Average Speed = 64 km / 11 hours

### Step 4: Simplifying the Average Speed
To get the average speed in a simpler form, we can divide:

**Average Speed ≈ 5.82 km/h**

### Final Answer
The average speed of the person is approximately **5.82 km/h**.

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