Two boys start running at the same time in the same direction at a speed of 10 km/hr and 12 km/hr respectively. In what time they will be 8 km apart?

Options

A. 6 hours
B. 5 hours
C. 4 hours
D. 3 hours

Answer

To solve the problem of how long it will take for the two boys to be 8 km apart, we can follow these steps:

### Step 1: Identify the speeds of the boys
- Boy 1's speed = 10 km/hr
- Boy 2's speed = 12 km/hr

### Step 2: Calculate the relative speed
Since both boys are running in the same direction, we need to find the relative speed. The relative speed is the difference between their speeds.

\[ \text{Relative Speed} = \text{Speed of Boy 2} - \text{Speed of Boy 1} = 12 \text{ km/hr} - 10 \text{ km/hr} = 2 \text{ km/hr} \]

### Step 3: Use the formula for time
We can use the formula for time, which is:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

In this case, the distance we want to find the time for is 8 km, and the speed is the relative speed we just calculated.

### Step 4: Substitute the values into the formula
\[ \text{Time} = \frac{8 \text{ km}}{2 \text{ km/hr}} = 4 \text{ hours} \]

### Conclusion
Thus, it will take 4 hours for the two boys to be 8 km apart.

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