What are the speeds of two objects if, when they move uniformly towards each other, they get 4 m closer in each second and when they move uniformly in the same direction with the original speeds, they get 4 m closer each 10 s?

Options

A. 2.8 m/s and 12 m/s
B. 5.2 m/s and 4.6 m/s
C. 3.2 m/s and 2.1 m/s
D. 2.2 m/s and 1.8 m/s

Explanation

To solve the problem, we need to determine the speeds of two objects based on the information provided about their relative motion. Let's denote the speeds of the two objects as \( V_1 \) and \( V_2 \).

### Step 1: Analyze the first scenario (moving towards each other)
When the two objects move towards each other, they get 4 meters closer each second. This means that the combined speed of the two objects is equal to 4 m/s. We can express this mathematically as:

\[ V_1 + V_2 = 4 \quad \text{(Equation 1)} \]

### Step 2: Analyze the second scenario (moving in the same direction)
When the two objects move in the same direction, they get 4 meters closer every 10 seconds. This means that their relative speed is such that they cover 4 meters in 10 seconds. Therefore, their relative speed can be calculated as:

\[ \text{Relative speed} = \frac{4 \text{ m}}{10 \text{ s}} = 0.4 \text{ m/s} \]

Since they are moving in the same direction, we can express this as:

\[ V_1 - V_2 = 0.4 \quad \text{(Equation 2)} \]

### Step 3: Solve the equations
Now we have two equations:

1. \( V_1 + V_2 = 4 \)
2. \( V_1 - V_2 = 0.4 \)

We can solve these equations simultaneously.

#### Adding the two equations:
\[ (V_1 + V_2) + (V_1 - V_2) = 4 + 0.4 \]
\[ 2V_1 = 4.4 \]
\[ V_1 = \frac{4.4}{2} = 2.2 \text{ m/s} \]

#### Substituting \( V_1 \) back into Equation 1:
Now we can find \( V_2 \):
\[ 2.2 + V_2 = 4 \]
\[ V_2 = 4 - 2.2 = 1.8 \text{ m/s} \]

### Final Answer
Thus, the speeds of the two objects are:
- \( V_1 = 2.2 \text{ m/s} \)
- \( V_2 = 1.8 \text{ m/s} \)