Two cars, A and B, are traveling in the same direction. Although car A is 186 m behind car B. The speed of A is 24.4 m/s, and the speed of B is 18.6 m/s. How much time does it take for A to catch B?

Options

A. 32.1 s
B. 11.8 s
C. 23.6 s
D. 8.33 s

Answer

To solve the problem of how long it takes for car A to catch up with car B, we can follow these steps:

### Step 1: Understand the problem
Car A is behind car B by a distance of 186 meters. Car A is moving faster than car B. We need to find the time it takes for car A to close this distance.

### Step 2: Identify the speeds of the cars
- Speed of car A, \( v_A = 24.4 \, \text{m/s} \)
- Speed of car B, \( v_B = 18.6 \, \text{m/s} \)

### Step 3: Calculate the relative speed
Since both cars are moving in the same direction, we can find the relative speed of car A with respect to car B:
\[ v_{\text{relative}} = v_A - v_B = 24.4 \, \text{m/s} - 18.6 \, \text{m/s} = 5.8 \, \text{m/s} \]

### Step 4: Use the relative speed to find the time
To find the time \( t \) it takes for car A to catch up to car B, we can use the formula:
\[ \text{Distance} = \text{Relative Speed} \times \text{Time} \]
Rearranging this formula to solve for time gives us:
\[ t = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{186 \, \text{m}}{5.8 \, \text{m/s}} \]

### Step 5: Calculate the time
Now we can perform the calculation:
\[ t = \frac{186}{5.8} \approx 32.06 \, \text{seconds} \]

### Conclusion
Therefore, it takes approximately 32.06 seconds for car A to catch up with car B.

---