Two cyclists A and B start cycling at 21 km/hr and 24 km/hr towards each other. They meet after 1 hour and 12 minutes. How far (in km) were they from each other when they started ?

Options

A. 48
B. 42
C. 54
D. 36

Answer

To solve the problem of finding the distance between the two cyclists when they started, we can follow these steps:

### Step 1: Convert the time into hours
The time given is 1 hour and 12 minutes. We need to convert this into hours.

- **Calculation**:
\[ 1 \text{ hour} + \frac{12 \text{ minutes}}{60 \text{ minutes/hour}} = 1 + 0.2 = 1.2 \text{ hours} \]

### Step 2: Determine the speeds of the cyclists
The speeds of cyclist A and cyclist B are given as 21 km/hr and 24 km/hr respectively.

### Step 3: Calculate the total speed
Since the two cyclists are moving towards each other, we can add their speeds to find the total speed at which they are approaching each other.

- **Calculation**:
\[ \text{Total Speed} = \text{Speed of A} + \text{Speed of B} = 21 \text{ km/hr} + 24 \text{ km/hr} = 45 \text{ km/hr} \]

### Step 4: Calculate the distance
Now that we have the total speed and the time taken until they meet, we can calculate the distance they were apart when they started.

- **Calculation**:
\[ \text{Distance} = \text{Total Speed} \times \text{Time} = 45 \text{ km/hr} \times 1.2 \text{ hours} = 54 \text{ km} \]

### Final Answer
The distance between the two cyclists when they started was **54 km**.

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