The speed of a boat in a river is 20 km/h and the speed of another boat is 23 km/h. They travel in the same direction from the same place at the same time. The distance between the boats after three and half hours is

Options

A. 11.5 km
B. 10 km
C. 10.5 km
D. 11 km

Answer

To solve the problem of finding the distance between two boats after three and a half hours, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the speeds of the boats:**
- Speed of Boat 1 (B1) = 20 km/h
- Speed of Boat 2 (B2) = 23 km/h

2. **Convert the time into hours:**
- Time = 3.5 hours (which can also be expressed as \( \frac{7}{2} \) hours)

3. **Calculate the distance traveled by Boat 1:**
- Distance traveled by Boat 1 = Speed × Time
- Distance (D1) = 20 km/h × \( \frac{7}{2} \) hours
- D1 = \( 20 \times \frac{7}{2} = \frac{140}{2} = 70 \) km

4. **Calculate the distance traveled by Boat 2:**
- Distance traveled by Boat 2 = Speed × Time
- Distance (D2) = 23 km/h × \( \frac{7}{2} \) hours
- D2 = \( 23 \times \frac{7}{2} = \frac{161}{2} = 80.5 \) km

5. **Find the distance between the two boats:**
- Distance between the boats (AB) = Distance traveled by Boat 2 - Distance traveled by Boat 1
- AB = D2 - D1
- AB = \( 80.5 \, \text{km} - 70 \, \text{km} = 10.5 \, \text{km} \)

### Final Answer:
The distance between the two boats after three and a half hours is **10.5 km**.

---