When two bodies move uniformly towards each other, the distance decrease by 6 m/s. If both the bodies moves (as above) in the same direction with the same speed, the distance between them increases by 4 m/s. Then the speed of the two bodies are :

Question

Accepted Answer

To determine the speeds of the two bodies, we need to analyze the given conditions:

1. **Condition 1: Moving Towards Each Other**
   - When the two bodies move uniformly towards each other, the distance between them decreases by 6 m/s. This means that the sum of their speeds is 6 m/s.

2. **Condition 2: Moving in the Same Direction**
   - When the two bodies move in the same direction with the same speeds, the distance between them increases by 4 m/s. This implies that the difference in their speeds is 4 m/s.

Let's denote the speed of the first body as $ v_1 $ and the speed of the second body as $ v_2 $.

From Condition 1:
$$ v_1 + v_2 = 6 $$

From Condition 2:
$$ v_1 - v_2 = 4 $$

We have a system of two linear equations:
1. $ v_1 + v_2 = 6 $
2. $ v_1 - v_2 = 4 $

To solve these equations, we can add them together:
$$ (v_1 + v_2) + (v_1 - v_2) = 6 + 4 $$
$$ 2v_1 = 10 $$
$$ v_1 = 5 $$

Substituting $ v_1 = 5 $ into the first equation:
$$ 5 + v_2 = 6 $$
$$ v_2 = 1 $$

Thus, the speeds of the two bodies are 5 m/s and 1 m/s, respectively. This corresponds to Option 2: 5 m/s, 1 m/s.

**Explanation of Why Other Options are Incorrect:**

- **Option 1: 7 m/s, 3 m/s**
  - If $ v_1 = 7 $ and $ v_2 = 3 $, then $ v_1 + v_2 = 10 $, which does not satisfy the condition $ v_1 + v_2 = 6 $.

- **Option 3: 4 m/s, 2 m/s**
  - If $ v_1 = 4 $ and $ v_2 = 2 $, then $ v_1 + v_2 = 6 $ is satisfied, but $ v_1 - v_2 = 2 $, which does not satisfy the condition $ v_1 - v_2 = 4 $.

- **Option 4: 3 m/s, 3 m/s**
  - If $ v_1 = 3 $ and $ v_2 = 3 $, then $ v_1 + v_2 = 6 $ is satisfied, but $ v_1 - v_2 = 0 $, which does not satisfy the condition $ v_1 - v_2 = 4 $.

Therefore, the only option that satisfies both conditions is Option 2: 5 m/s, 1 m/s.