Sonu and Monu travel from point P to Q, a distance of 42 km, at 6 km/h and 8 km/h, respectively. Monu reaches Q first and returns immediately and meets Sonu at R. Find the dis- tance from pointsPtoR.

Answer

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

### Step 1: Understand the Problem
Sonu and Monu are traveling from point P to Q, which is a distance of 42 km. Sonu's speed is 6 km/h and Monu's speed is 8 km/h. Monu reaches Q first, returns, and meets Sonu at point R. We need to find the distance from P to R.

### Step 2: Calculate the Time Taken by Each Traveler to Reach Q
- **Time taken by Sonu to reach Q**:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{42 \text{ km}}{6 \text{ km/h}} = 7 \text{ hours} \]

- **Time taken by Monu to reach Q**:
\[ \text{Time} = \frac{42 \text{ km}}{8 \text{ km/h}} = 5.25 \text{ hours} \]

### Step 3: Determine How Long Monu Waits at Q
Monu reaches Q first and waits for Sonu to arrive. The time Monu waits at Q is:
\[ \text{Wait time} = \text{Time taken by Sonu} - \text{Time taken by Monu} = 7 \text{ hours} - 5.25 \text{ hours} = 1.75 \text{ hours} \]

### Step 4: Calculate the Distance Monu Travels Back to Meet Sonu
During the time Monu waits, he travels back towards Sonu. The distance Monu travels back in 1.75 hours at a speed of 8 km/h is:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 8 \text{ km/h} \times 1.75 \text{ hours} = 14 \text{ km} \]

### Step 5: Calculate the Distance from P to R
Since Monu travels back 14 km towards Sonu, the distance from P to R can be calculated as:
\[ \text{Distance from P to R} = 42 \text{ km} - 14 \text{ km} = 28 \text{ km} \]

### Final Answer
The distance from point P to point R is **28 km**.

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