Sarita and Julie start walking from the same place in the opposite directions. If julie walks at a speed of `2(1)/(2)` km/hr and Sarita at a speed of 2 km/hr, in how much time will they be 18 km apart?

Options

A. 4.0 hrs
B. 4.5hrs
C. 5.0 hrs
D. 4.8 hrs

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Identify the speeds of Sarita and Julie
- Julie's speed = \(2 \frac{1}{2}\) km/hr = \(2.5\) km/hr
- Sarita's speed = \(2\) km/hr

### Step 2: Calculate the relative speed
Since Sarita and Julie are walking in opposite directions, we can add their speeds to find the relative speed.
- Relative speed = Julie's speed + Sarita's speed
- Relative speed = \(2.5\) km/hr + \(2\) km/hr = \(4.5\) km/hr

### Step 3: Use the formula for distance
We know the formula for distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
We need to find the time when they are \(18\) km apart.

### Step 4: Rearrange the formula to find time
From the distance formula, we can rearrange it to find time:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

### Step 5: Substitute the values into the formula
Substituting the known values into the formula:
\[ \text{Time} = \frac{18 \text{ km}}{4.5 \text{ km/hr}} \]

### Step 6: Calculate the time
Now, we perform the division:
\[ \text{Time} = \frac{18}{4.5} = 4 \text{ hours} \]

### Final Answer
Thus, Sarita and Julie will be \(18\) km apart in **4 hours**.

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