A starts from P to walk in Q a distance of 51.75 km at the rate of 3.75km an hour.An hour latter B starts from Q for P and walk at the rate of 4.25 km an hour. when and where will meet B?

Options

A. 26.25km from Q
B. 25.50km from Q
C. 25.30 km from P
D. can not be determined

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Problem
A starts walking from point P to point Q, which is a distance of 51.75 km at a speed of 3.75 km/h. One hour later, B starts walking from point Q to point P at a speed of 4.25 km/h. We need to find out when and where A and B will meet.

### Step 2: Calculate the Distance Covered by A Before B Starts
Since B starts one hour later, we first calculate how far A has walked in that hour.

- Speed of A = 3.75 km/h
- Time before B starts = 1 hour

Distance covered by A in 1 hour:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 3.75 \text{ km/h} \times 1 \text{ h} = 3.75 \text{ km} \]

### Step 3: Determine the Remaining Distance for A
After 1 hour, A has covered 3.75 km, so the remaining distance to Q is:
\[ \text{Remaining distance} = 51.75 \text{ km} - 3.75 \text{ km} = 48 \text{ km} \]

### Step 4: Set Up the Relative Speed
Now, A is 3.75 km away from the starting point P when B starts. The speeds of A and B are:
- Speed of A = 3.75 km/h
- Speed of B = 4.25 km/h

Since they are moving towards each other, we can add their speeds to find the relative speed:
\[ \text{Relative Speed} = \text{Speed of A} + \text{Speed of B} = 3.75 \text{ km/h} + 4.25 \text{ km/h} = 8 \text{ km/h} \]

### Step 5: Calculate the Time Until They Meet
Now, we need to find out how long it will take for A and B to meet after B starts walking. The distance between them when B starts is 48 km.

Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]
\[ \text{Time} = \frac{48 \text{ km}}{8 \text{ km/h}} = 6 \text{ hours} \]

### Step 6: Calculate the Meeting Point
Now we know that B will meet A after 6 hours. We can calculate how far B travels in that time:
\[ \text{Distance traveled by B} = \text{Speed of B} \times \text{Time} \]
\[ \text{Distance traveled by B} = 4.25 \text{ km/h} \times 6 \text{ h} = 25.5 \text{ km} \]

### Conclusion
Thus, A and B will meet 25.5 km from point Q.

### Final Answer
**A and B will meet 25.5 km from Q.**

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