Two cars travelling in parallel lanes at 90 kph and 72 kph. Assuming each car to be 5 m long, find the time taken during the overtake and the total road distance used for the overtake

Answer

To solve the problem of two cars overtaking each other, we will follow these steps:

### Step 1: Determine the speeds of the cars in meters per second (m/s).
- The speed of the first car is 90 km/h.
- The speed of the second car is 72 km/h.

To convert these speeds into meters per second, we use the conversion factor:
\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]

Calculating the speeds:
- Speed of the first car:
\[ 90 \text{ km/h} = 90 \times \frac{5}{18} = 25 \text{ m/s} \]
- Speed of the second car:
\[ 72 \text{ km/h} = 72 \times \frac{5}{18} = 20 \text{ m/s} \]

### Step 2: Calculate the relative speed of the two cars.
Since the first car is overtaking the second car, we find the relative speed by subtracting the speed of the second car from the speed of the first car:
\[ \text{Relative Speed} = 25 \text{ m/s} - 20 \text{ m/s} = 5 \text{ m/s} \]

### Step 3: Determine the total distance that needs to be covered for the overtaking maneuver.
The total distance to be covered during the overtaking is the length of both cars:
\[ \text{Total Distance} = \text{Length of Car 1} + \text{Length of Car 2} = 5 \text{ m} + 5 \text{ m} = 10 \text{ m} \]

### Step 4: Calculate the time taken to overtake.
Using the formula for time, which is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
we can substitute the values:
\[ \text{Time} = \frac{10 \text{ m}}{5 \text{ m/s}} = 2 \text{ seconds} \]

### Step 5: Calculate the total road distance used during the overtake.
To find the total road distance used, we need to consider the distance traveled by the first car during the overtaking time:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Using the speed of the first car:
\[ \text{Distance} = 25 \text{ m/s} \times 2 \text{ s} = 50 \text{ m} \]

### Step 6: Add the distance covered by the second car.
Since the second car is also moving during the overtaking:
\[ \text{Distance} = 20 \text{ m/s} \times 2 \text{ s} = 40 \text{ m} \]

However, the total distance used for the overtaking maneuver is simply the distance covered by the first car plus the length of the second car:
\[ \text{Total Road Distance} = 50 \text{ m} + 5 \text{ m} = 55 \text{ m} \]

### Final Answer:
- Time taken during the overtake: **2 seconds**
- Total road distance used for the overtake: **55 meters**

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