A car is ahead a motor cyclist by 40 km, the car is running at 40 km/h and the motor cyclist at 50 km/h. After how much time motor cyclist cross the car?

Options

A. 3 h
B. 4 h
C. `3 1/2` h
D. 2.4 h

Answer

To solve the problem of when the motorcyclist will cross the car, we can follow these steps:

### Step 1: Understand the situation
The car is ahead of the motorcyclist by 40 km. The car is moving at a speed of 40 km/h, while the motorcyclist is moving at a speed of 50 km/h.

### Step 2: Determine the relative speed
To find out how quickly the motorcyclist is gaining on the car, we need to calculate the relative speed between the motorcyclist and the car.

\[ \text{Relative Speed} = \text{Speed of Motorcyclist} - \text{Speed of Car} \]
\[ \text{Relative Speed} = 50 \text{ km/h} - 40 \text{ km/h} = 10 \text{ km/h} \]

### Step 3: Calculate the time taken to close the gap
Now that we know the motorcyclist is gaining on the car at a rate of 10 km/h, we can calculate how long it will take for the motorcyclist to close the 40 km gap.

Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
we can substitute the values:
\[ \text{Time} = \frac{40 \text{ km}}{10 \text{ km/h}} = 4 \text{ hours} \]

### Conclusion
The motorcyclist will cross the car after 4 hours.

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