Two cars leave the same place at the same time. One runs at 20 km/ hr towards north and the other at 15 km/hr towards east. What will be the distance between them (in km) after 2 hours of travelling?

Options

A. 25
B. 50
C. 70
D. 10

Explanation

To solve the problem of finding the distance between the two cars after 2 hours of traveling, we can follow these steps:

### Step 1: Calculate the distance traveled by each car.
- **Car 1** (North): The speed is 20 km/hr.
- Distance traveled in 2 hours = Speed × Time = 20 km/hr × 2 hr = 40 km.

- **Car 2** (East): The speed is 15 km/hr.
- Distance traveled in 2 hours = Speed × Time = 15 km/hr × 2 hr = 30 km.

### Step 2: Visualize the scenario.
- After 2 hours, Car 1 is 40 km north of the starting point, and Car 2 is 30 km east of the starting point. This forms a right triangle where:
- One leg (north) = 40 km
- Other leg (east) = 30 km

### Step 3: Use the Pythagorean theorem to find the distance between the two cars.
- According to the Pythagorean theorem, the distance \( D \) between the two cars can be calculated as:
\[ D = \sqrt{(40 \text{ km})^2 + (30 \text{ km})^2} \]

### Step 4: Calculate the squares and sum them.
- Calculate \( 40^2 \) and \( 30^2 \):
\[ 40^2 = 1600 \quad \text{and} \quad 30^2 = 900 \]
- Now sum these values:
\[ 1600 + 900 = 2500 \]

### Step 5: Take the square root to find the distance.
- Finally, take the square root of the sum:
\[ D = \sqrt{2500} = 50 \text{ km} \]

### Conclusion:
The distance between the two cars after 2 hours of traveling is **50 km**.

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