B starts 4.5 minutes after A from the same point, for a place at a distance of 3.5 miles from the starting point. A on reaching the destination turns back and walk a mile where he meets B. If A's speed is a mile in 6 minutes then B's speed is a mile in_____minutes ?

Options

A. 8
B. 10
C. 12
D. 9

Answer

To solve the problem step by step, we need to analyze the situation involving A and B's movements.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- A starts walking towards a destination that is 3.5 miles away.
- B starts 4.5 minutes after A.
- A walks to the destination, turns back, and walks 1 mile towards B before they meet.

2. **A's Speed**:
- A's speed is given as 1 mile in 6 minutes.
- This means A covers 1 mile in 6 minutes.

3. **Time Taken by A to Reach the Destination**:
- The distance to the destination is 3.5 miles.
- Time taken by A to reach the destination = Distance / Speed = 3.5 miles / (1 mile / 6 minutes) = 3.5 * 6 = 21 minutes.

4. **Time Taken by A to Walk Back 1 Mile**:
- After reaching the destination, A turns back and walks 1 mile.
- Time taken by A to walk back 1 mile = 1 mile / (1 mile / 6 minutes) = 6 minutes.

5. **Total Time for A until Meeting B**:
- Total time from the start until A meets B = Time to reach destination + Time to walk back 1 mile = 21 minutes + 6 minutes = 27 minutes.

6. **Time Taken by B**:
- B starts 4.5 minutes after A, so by the time A has walked for 27 minutes, B has been walking for:
- Time B has walked = Total time A walked - B's delay = 27 minutes - 4.5 minutes = 22.5 minutes.

7. **Distance Covered by A and B**:
- When A meets B, A has walked a total distance of 3.5 miles (to the destination) + 1 mile (back towards B) = 4.5 miles.
- B has covered the distance from the starting point to the meeting point, which is the distance A has walked back (1 mile) plus the distance B has covered while A was walking to the destination (3.5 miles - 1 mile = 2.5 miles). Thus, B has traveled 2.5 miles.

8. **Calculating B's Speed**:
- Speed of B = Distance / Time = 2.5 miles / 22.5 minutes.
- To find B's speed in miles per minute:
- 2.5 miles / 22.5 minutes = 1/9 miles per minute.

9. **Converting Speed to Minutes per Mile**:
- If B's speed is 1/9 miles per minute, then the time taken by B to cover 1 mile = 1 / (1/9) = 9 minutes.

### Final Answer:
B's speed is 1 mile in **9 minutes**.