Two cars move in the same direction along parallel roads. One of them is a `200m`, long travelling with a velocity of `20m//s`. The second one is `800m` long travelling with a velocity of `7.5m//s`. How long will it take for the first car to overtake the second car?

Options

A. 20 s
B. 40 s
C. 60 s
D. 80 s

Answer

To solve the problem of how long it will take for the first car to overtake the second car, we can follow these steps:

### Step 1: Identify the lengths and velocities of the cars
- Length of the first car (Car A), \( L_1 = 200 \, \text{m} \)
- Length of the second car (Car B), \( L_2 = 800 \, \text{m} \)
- Velocity of the first car (Car A), \( V_1 = 20 \, \text{m/s} \)
- Velocity of the second car (Car B), \( V_2 = 7.5 \, \text{m/s} \)

### Step 2: Calculate the total distance to be covered
To overtake the second car, the first car must cover its own length plus the length of the second car:
\[ \text{Total distance} = L_1 + L_2 = 200 \, \text{m} + 800 \, \text{m} = 1000 \, \text{m} \]

### Step 3: Calculate the relative velocity
Since both cars are moving in the same direction, the relative velocity of the first car with respect to the second car is:
\[ \text{Relative velocity} = V_1 - V_2 = 20 \, \text{m/s} - 7.5 \, \text{m/s} = 12.5 \, \text{m/s} \]

### Step 4: Calculate the time taken to overtake
The time taken to overtake can be calculated using the formula:
\[ \text{Time} = \frac{\text{Total distance}}{\text{Relative velocity}} = \frac{1000 \, \text{m}}{12.5 \, \text{m/s}} \]
Calculating this gives:
\[ \text{Time} = 80 \, \text{s} \]

### Final Answer
The time taken for the first car to overtake the second car is **80 seconds**.

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