Two cyclists A and B start from the same place at the same time one going towards north at 18 km/hr and other going towards south at 20km/hr what time will they take to be 95 km apart

Options

A. 4hr 30min
B. 4 hr 45 min
C. 5 hrs 16 min
D. 2 hrs.30 min

Answer

To solve the problem of how long it will take for the two cyclists A and B to be 95 km apart, we can follow these steps:

### Step 1: Determine the speeds of the cyclists.
- Cyclist A is traveling north at a speed of 18 km/hr.
- Cyclist B is traveling south at a speed of 20 km/hr.

### Step 2: Calculate the combined speed of both cyclists.
Since they are moving in opposite directions, we can add their speeds together to find the rate at which the distance between them is increasing:
- Combined speed = Speed of A + Speed of B
- Combined speed = 18 km/hr + 20 km/hr = 38 km/hr

### Step 3: Use the formula for time.
We can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
In this case, the distance we want them to be apart is 95 km, and the combined speed is 38 km/hr.

### Step 4: Calculate the time taken to be 95 km apart.
- Time = Distance / Combined Speed
- Time = 95 km / 38 km/hr

### Step 5: Perform the division.
Calculating the time:
\[ \text{Time} = \frac{95}{38} \approx 2.5 \text{ hours} \]

### Step 6: Convert hours into hours and minutes.
- 0.5 hours = 30 minutes
- Therefore, 2.5 hours = 2 hours and 30 minutes.

### Final Answer:
The two cyclists will take **2 hours and 30 minutes** to be 95 km apart.

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