Two toy cars X and Y run at average speed of 0.5 km/hr and 1.5 km/hr respectively. If car X moves in South direction and toy Y in East direction beginning from the same origin at the same time, what will be the distance between the two after 4 hours?

Options

A. 7 km
B. `2sqrt(10)` km
C. `sqrt(39)` km
D. `sqrt(19)` km

Answer

To find the distance between the two toy cars X and Y after 4 hours, we can follow these steps:

### Step 1: Determine the distance traveled by each car
- **Car X** moves at a speed of 0.5 km/hr.
- **Car Y** moves at a speed of 1.5 km/hr.
- Both cars travel for 4 hours.

**Distance traveled by Car X:**
\[ \text{Distance}_X = \text{Speed}_X \times \text{Time} = 0.5 \, \text{km/hr} \times 4 \, \text{hr} = 2 \, \text{km} \]

**Distance traveled by Car Y:**
\[ \text{Distance}_Y = \text{Speed}_Y \times \text{Time} = 1.5 \, \text{km/hr} \times 4 \, \text{hr} = 6 \, \text{km} \]

### Step 2: Visualize the positions of the cars
- Car X moves south and ends up 2 km south of the origin.
- Car Y moves east and ends up 6 km east of the origin.

### Step 3: Form a right triangle
- The position of Car X (2 km south) and Car Y (6 km east) forms a right triangle where:
- One leg (south) = 2 km (distance of Car X)
- Other leg (east) = 6 km (distance of Car Y)

### Step 4: Apply the Pythagorean theorem
To find the distance \( d \) between the two cars, we can use the Pythagorean theorem:
\[ d^2 = (2 \, \text{km})^2 + (6 \, \text{km})^2 \]

Calculating:
\[ d^2 = 4 + 36 = 40 \]
\[ d = \sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10} \, \text{km} \]

### Step 5: Conclusion
The distance between the two toy cars after 4 hours is:
\[ d = 2\sqrt{10} \, \text{km} \]

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