A car driver is driving at a speed of 88 kmph. A bus which is 100 m away from the car and traveling at speed of 52 km/h. The time taken by car to leave the bus 200 m behind is

Options

A. 25 sec
B. 30 sec
C. 32 sec
D. 28 sec

Answer

To solve the problem step by step, we need to find out how long it will take for the car to leave the bus 200 meters behind.

### Step 1: Understand the initial conditions
- The car is traveling at a speed of 88 km/h.
- The bus is 100 meters ahead of the car and is traveling at a speed of 52 km/h.

### Step 2: Convert speeds from km/h to m/s
To work with the distances in meters, we need to convert the speeds from kilometers per hour to meters per second using the conversion factor (1 km/h = 5/18 m/s).

- Speed of the car in m/s:
\[ 88 \text{ km/h} = 88 \times \frac{5}{18} = \frac{440}{18} \approx 24.44 \text{ m/s} \]

- Speed of the bus in m/s:
\[ 52 \text{ km/h} = 52 \times \frac{5}{18} = \frac{260}{18} \approx 14.44 \text{ m/s} \]

### Step 3: Calculate the relative speed
Since both vehicles are moving in the same direction, the relative speed of the car with respect to the bus is:
\[ \text{Relative Speed} = \text{Speed of Car} - \text{Speed of Bus} = 24.44 \text{ m/s} - 14.44 \text{ m/s} = 10 \text{ m/s} \]

### Step 4: Determine the total distance to be covered
The car needs to cover the initial distance of 100 meters to reach the bus and then an additional 200 meters to leave the bus behind. Therefore, the total distance the car needs to cover is:
\[ \text{Total Distance} = 100 \text{ m} + 200 \text{ m} = 300 \text{ m} \]

### Step 5: Calculate the time taken to cover the distance
Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
we can find the time taken by the car to cover 300 meters at the relative speed of 10 m/s:
\[ \text{Time} = \frac{300 \text{ m}}{10 \text{ m/s}} = 30 \text{ seconds} \]

### Final Answer
The time taken by the car to leave the bus 200 meters behind is **30 seconds**.

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